UPDATE (March 2020, thanks @ic): I don't know the exact AMI version but yum install docker now works on the latest Amazon Linux 2. The instructions below may still be relevant depending on the vintage AMI you are using.
Amazon changed the install in Linux 2. One no-longer using 'yum' See: https://aws.amazon.com/amazon-linux-2/release-notes/
sudo amazon-linux-extras install docker
sudo service docker start
sudo usermod -a -G docker ec2-userMake docker auto-start
sudo chkconfig docker on
Because you always need it....
sudo yum install -y git
Reboot to verify it all loads fine on its own.
sudo reboot
Copy the appropriate docker-compose binary from GitHub:
sudo curl -L https://github.com/docker/compose/releases/download/1.22.0/docker-compose-$(uname -s)-$(uname -m) -o /usr/local/bin/docker-compose
NOTE: to get the latest version (thanks @spodnet):
sudo curl -L https://github.com/docker/compose/releases/latest/download/docker-compose-$(uname -s)-$(uname -m) -o /usr/local/bin/docker-compose
Fix permissions after download:
sudo chmod +x /usr/local/bin/docker-compose
Verify success:
docker-compose version