EDIT (2023): Do not keep using docker-compose! Please migrate to docker compose, which is now part of the docker image and a 99% drop-in replacement of docker-compose. Ironically, if you (now) use docker:latest, the question does not apply. See Docker's documentation on Compose V2. The answer below only applies to docker-compose, AKA Compose V1, which is to be discontinued/become unsupported.

Docker also provides an official docker-compose image: docker/compose

This is the ideal solution if you don't want to install it every pipeline.

Note that in the latest version of GitLab CI/Docker you will likely need to give privileged access to your GitLab CI Runner and configure/disable TLS. See Use docker-in-docker workflow with Docker executor

variables:
  DOCKER_HOST: tcp://docker:2375/
  DOCKER_DRIVER: overlay2

# Official docker compose image.
image:
  name: docker/compose:latest

services:
  - docker:dind

before_script:
  - docker version
  - docker-compose version

build:
  stage: build
  script:
    - docker-compose down
    - docker-compose build
    - docker-compose up tester-image

Note that in versions of docker-compose earlier than 1.25:

Since the image uses docker-compose-entrypoint.sh as entrypoint you'll need to override it back to /bin/sh -c in your .gitlab-ci.yml. Otherwise your pipeline will fail with No such command: sh

    image:
      name: docker/compose:latest
      entrypoint: ["/bin/sh", "-c"]