The 28-year-old played for Benfica for six years, making 251 appearances and scoring 41 goals for the Portuguese club.
The Argentina international declared his delight at moving to the Champions League runners-up.
"I know that Atletico has been interested in me for some years. It is one of the reasons that led me to make the decision to come here," he said
"They have followed me for several years. With the national team I would ask my colleagues about Atletico.
"I will be able to bring with me the sense of tactical order I learned in Portugal," Gaitan added.
Will Gaitan help Atletico challenge for domestic and European honours?