The Ghana international has signed a six-year deal at the Vicente Calderon but will spend next season on loan at Getafe.
A statement on Atletico's website read: "Bernard Mensah is an Atletico Madrid player after an agreement was reached with Guimarares.
"The midfielder is known for his speed and driving with the ball. At 20 he is already a full international for Ghana."
Mensah made 30 appearances for Portuguese club Guimaraes last season, scoring five goals.
He becomes Atletico's second signing in the space of three days after they confirmed the arrival of defender Stefan Savic from Fiorentina on Monday.