The Argentine international is currently on loan at the Spanish champions from Zenit St Petersburg, and under the current agreement will return to Russia next summer.
However, the 27-year-old has revealed that he wants to remain in La Liga on a long-term basis.
"I needed a change. I spoke to the coach at Zenit and he told me he was going to give priority in my position to somebody else, although he was still counting on me but not as much," he told Marca.
"I understood and told him that as Atletico were interested I would rather go there and fight for a place knowing I was going to a great team.
"My idea is not to return to Russia and if it's possible I want to stay here because I already feel at home. I'm enjoying the climate, the country, the language... they are small things but very important."
Ansaldi joined Zenit from Rubin Kazan in 2013.