This page contains all the information you need on how to complete the romance with Garrus Vakarian.
Once you’ve completed the necessary steps to continuing the romance with Garrus which can be found here, How To Start Garrus Romance. Progress through the game until you’re ready to initiate the mission, Priority: Cerberus Headquarters and then Garrus will meet with you in your cabin.
Here you’ll want to say “Yes, please stay” and you two will engage in an intimate moment together. After this, you’ll be saying your final goodbyes to Garrus during the Priority: Earth.