Another approach is to use:

enumerated()

Update for Swift 6.2:

Swift 6.2 introduces Collection conformances for enumerated(). (SE-0459)

ForEach(array.enumerated(), id: \.offset) { index, element in
  // ...
}

Before Swift 6.2:

ForEach(Array(array.enumerated()), id: \.offset) { index, element in
  // ...
}

Source: https://alejandromp.com/blog/swiftui-enumerated/

I usually use enumerated to get a pair of index and element with the element as the id

ForEach(Array(array.enumerated()), id: \.element) { index, element in
    Text("\(index)")
    Text(element.description)
}

For a more reusable component, you can visit this article https://onmyway133.com/posts/how-to-use-foreach-with-indices-in-swiftui/

I needed a more generic solution, that could work on all kind of data (that implements RandomAccessCollection), and also prevent undefined behavior by using ranges.
I ended up with the following:

public struct ForEachWithIndex<Data: RandomAccessCollection, ID: Hashable, Content: View>: View {
    public var data: Data
    public var content: (_ index: Data.Index, _ element: Data.Element) -> Content
    var id: KeyPath<Data.Element, ID>

    public init(_ data: Data, id: KeyPath<Data.Element, ID>, content: @escaping (_ index: Data.Index, _ element: Data.Element) -> Content) {
        self.data = data
        self.id = id
        self.content = content
    }

    public var body: some View {
        ForEach(
            zip(self.data.indices, self.data).map { index, element in
                IndexInfo(
                    index: index,
                    id: self.id,
                    element: element
                )
            },
            id: \.elementID
        ) { indexInfo in
            self.content(indexInfo.index, indexInfo.element)
        }
    }
}

extension ForEachWithIndex where ID == Data.Element.ID, Content: View, Data.Element: Identifiable {
    public init(_ data: Data, @ViewBuilder content: @escaping (_ index: Data.Index, _ element: Data.Element) -> Content) {
        self.init(data, id: \.id, content: content)
    }
}

extension ForEachWithIndex: DynamicViewContent where Content: View {
}

private struct IndexInfo<Index, Element, ID: Hashable>: Hashable {
    let index: Index
    let id: KeyPath<Element, ID>
    let element: Element

    var elementID: ID {
        self.element[keyPath: self.id]
    }

    static func == (_ lhs: IndexInfo, _ rhs: IndexInfo) -> Bool {
        lhs.elementID == rhs.elementID
    }

    func hash(into hasher: inout Hasher) {
        self.elementID.hash(into: &hasher)
    }
}

This way, the original code in the question can just be replaced by:

ForEachWithIndex(array, id: \.self) { index, item in
  CustomView(item: item)
    .tapAction {
      self.doSomething(index) // Now works
    }
}

To get the index as well as the element.

Note that the API is mirrored to that of SwiftUI - this means that the initializer with the id parameter's content closure is not a @ViewBuilder.
The only change from that is the id parameter is visible and can be changed

For non zero based arrays avoid using enumerated, instead use zip:

ForEach(Array(zip(items.indices, items)), id: \.0) { index, item in
  // Add Code here
}

I created a dedicated View for this purpose:

struct EnumeratedForEach<ItemType, ContentView: View>: View {
    let data: [ItemType]
    let content: (Int, ItemType) -> ContentView

    init(_ data: [ItemType], @ViewBuilder content: @escaping (Int, ItemType) -> ContentView) {
        self.data = data
        self.content = content
    }

    var body: some View {
        ForEach(Array(zip(data.indices, data)), id: \.0) { idx, item in
            content(idx, item)
        }
    }
}

Now you can use it like this:

EnumeratedForEach(items) { idx, item in
    ...
}

As mentioned in comments by Robin Daugherty it's not a good practice to identify elements by their index in the array – it's fine sometimes but not when you want to reorder or insert/remove elements. Therefore if you want to do it right – conform ItemType to Identifiable (it's up to you then to identify each element properly) and use the element itself in the ForEach as an id, like this (notice id: \.1 instead of id: \.0):

ForEach(Array(zip(data.indices, data)), id: \.1) { idx, item in
    content(idx, item)
}

Small note: \.0 and \.1 correspond to element from the first array you pass to zip and element from the second array respectively. It's coming from the tuple from array of tuples, created when you write Array(zip(..., ...)).

In this example since we pass data.indices as the first array, \.0 is index and \.1 is the element itself, since the second array we pass is just array of elements – data

You can use this method:

.enumerated()

From the Swift documentation:

Returns a sequence of pairs (n, x), where n represents a consecutive integer starting at zero and x represents an element of the sequence.

var elements: [String] = ["element 1", "element 2", "element 3", "element 4"]

ForEach(Array(elements.enumerated()), id: \.element) { index, element in
  Text("\(index) \(element)")
}

ForEach is SwiftUI isn’t the same as a for loop, it’s actually doing something called structural identity. The documentation of ForEach states:

/// It's important that the `id` of a data element doesn't change, unless
/// SwiftUI considers the data element to have been replaced with a new data
/// element that has a new identity.

This means we cannot use indices, enumerated or a new Array in the ForEach. The ForEach must be given the actual array of identifiable items. This is so SwiftUI can animate the rows around to match the data, obviously this can't work with indicies, e.g. if row at 0 is moved to 1 its index is still 0.

To solve your problem of getting the index, you simply have to look up the index like this:

ForEach(items) { item in
  CustomView(item: item)
    .tapAction {
      if let index = array.firstIndex(where: { $0.id == item.id }) {
          self.doSomething(index) 
      }
    }
}

You can see Apple doing this in their Scrumdinger sample app tutorial.

guard let scrumIndex = scrums.firstIndex(where: { $0.id == scrum.id }) else {
    fatalError("Can't find scrum in array")
}

The advantage of the following approach is that the views in ForEach even change if state values ​​change:

struct ContentView: View {
    @State private var array = [1, 2, 3]

    func doSomething(index: Int) {
        self.array[index] = Int.random(in: 1..<100)
    }

    var body: some View {    
        let arrayIndexed = array.enumerated().map({ $0 })

        return List(arrayIndexed, id: \.element) { index, item in

            Text("\(item)")
                .padding(20)
                .background(Color.green)
                .onTapGesture {
                    self.doSomething(index: index)
            }
        }
    }
}

... this can also be used, for example, to remove the last divider in a list:

struct ContentView: View {

    init() {
        UITableView.appearance().separatorStyle = .none
    }

    var body: some View {
        let arrayIndexed = [Int](1...5).enumerated().map({ $0 })

        return List(arrayIndexed, id: \.element) { index, number in

            VStack(alignment: .leading) {
                Text("\(number)")

                if index < arrayIndexed.count - 1 {
                    Divider()
                }
            }
        }
    }
}

2021 solution if you use non zero based arrays avoid using enumerated:

ForEach(array.indices,id:\.self) { index in
    VStack {
        Text(array[index].name)
            .customFont(name: "STC", style: .headline)
            .foregroundColor(Color.themeTitle)
        }
    }
}

To get indexing from SwiftUI's ForEach loop, you could use closure's shorthand argument names:

@State private var cars = ["Aurus","Bentley","Cadillac","Genesis"]

var body: some View {
    NavigationView {
        List {
            ForEach(Array(cars.enumerated()), id: \.offset) {

                Text("\($0.element) at \($0.offset) index")
            }
        }
    }
}

Results:

//   Aurus at 0 index
//   Bentley at 1 index
//   Cadillac at 2 index
//   Genesis at 3 index

P. S.

Initially, I posted an answer with a "common" expression that all Swift developers are used to, however, thanks to @loremipsum I changed it. As stated in WWDC 2021 Demystify SwiftUI video (time 33:40), array indices are not stable from \.self identity (key path).

ForEach(0 ..< cars.count, id: \.self) {     // – NOT STABLE
    Text("\(cars[$0]) at \($0) index")
}

I use extension ForEach to resolve this issue:

extension ForEach {
  
  public init<T: RandomAccessCollection>(
    data: T,
    content: @escaping (T.Index, T.Element) -> Content
  ) where T.Element: Identifiable, T.Element: Hashable, Content: View, Data == [(T.Index, T.Element)], ID == T.Element  {
    self.init(Array(zip(data.indices, data)), id: \.1) { index, element in
      content(index, element)
    }
  }
}

How to using:

ForEach(data: array) { index, element in
    Text("\(index)")
    Text(element.description)
}

Here is a simple solution though quite inefficient to the ones above..

In your Tap Action, pass through your item

.tapAction {

   var index = self.getPosition(item)

}

Then create a function the finds the index of that item by comparing the id

func getPosition(item: Item) -> Int {

  for i in 0..<array.count {
        
        if (array[i].id == item.id){
            return i
        }
        
    }
    
    return 0
}