Setting up node with redis using docker-compose

I have an Express app and React app, and in the backend part I'm using Redis. I setup one Dockerfile for the frontend, and one for the backend. Additionally, I setup the docker-compose.yml file, which looks like this:

# Specify docker-compose version.
version: '3'

# Define the services/containers to be run.
services:
  react:
    build: admin
    ports:
      - '3000:3000'

  express:
    build: .
    container_name: api
    ports:
      - '3001:3001'
    depends_on:
      - redis
    links:
      - mongo
      - redis
    environment:
      - REDIS_URL=redis://cache
      - MONGO_URL=mongodb://db/tests

  mongo:
    image: mongo:4
    container_name: db
    ports:
      - '27017:27017'

  redis:
    image: redis:4
    container_name: cache
    ports:
      - '6379:6379'

And inside my backend, I call redisClient as follows:

const bluebird = require('bluebird');
const config   = require('config');
const logger   = require('./logger');
const redis    = require('redis');
bluebird.promisifyAll(redis);

const RedisService = function() {
    const redisConnectionString = process.env.REDIS_URL;
    this.client = redis.createClient({ url: redisConnectionString });
    this.client.on('error', (err) => {
        logger.error(err);
    });
};

Where config reads the .json file inside my config folder. However, when I run docker-compose up, it throws the following error:

express_1  | [2019-06-10T20:14:38.169Z] error: "uncaughtException: Redis connection to 127.0.0.1:6379 failed - connect ECONNREFUSED 127.0.0.1:6379
Error: Redis connection to 127.0.0.1:6379 failed - connect ECONNREFUSED 127.0.0.1:6379
    at TCPConnectWrap.afterConnect [as oncomplete] (net.js:1106:14) 

Any ideas how to properly connect Redis with docker-compose in my setting where I read the connection string from the config .json file?