I have successfully deployed my laravel 5 app to AWS EC2. I have also created a MySQL database with AWS RDS and associated it with my app instance.
Now I want to set my
You could create a new .env on your ec2 instance and add all the env vars in there. One option would be ssh-ing into the box and creating the file via vi or cat. Or you could write a script to remotely pull the .env in from an external location.
You could also ssh into the box and export APP_ENV=production all your env vars (assuming that's the right command for your OS).
Adding env vars to your environment will depend on the OS that your ec2 instance is running, so the solution will depend on that. ec2 has a concept of 'tags' which might be useful, but the docs show they limit the number of tags to 10, so you may have to do it manually and per ec2 instance :/
See here for one method that uses tags to pull in and set env vars (non-laravel specific).
I just went through this yesterday while getting Laravel running on Elastic Beanstalk, the solution was clean. You can actually set the env vars directly via the aws console (EB app/environment -> Configuration -> Software Configuration -> Environment Properties).
Update:
The key concept to understand is that Laravel just uses phpdotenv to dump vars from the .env file into php's global $_ENV, whereas any already existing env vars are automatically included in $_ENV when php starts the server (docs). So the .env file itself is unnecessary, really just a dev convenience. (unless I've just been spoiled by elastic beanstalk so far).