The 18-year-old was officially unveiled as the La Liga club's latest acquisition on Wednesday, as he penned a five-year contract.
Gimenez becomes the fourth addition at Atletico this summer, with deals for David Villa, Martin Demichelis and Leo Baptistao having already been sealed.
The youngster cannot wait to get started in European football and is expecting to learn plenty from experienced Uruguayan compatriot Diego Godin at Vicente Calderon.
He said on his arrival in Spain: "This is a dream, I'm so happy.
"I love to fight for every ball as if it is the last minute of a game and I am the type of player who never abandons my team-mates.
"I have come here to grow.
"Diego Godin is one the reference points of the Uruguayan national team and I'm looking forward to learning a lot from him."