The 33-year-old midfielder will spend the rest of the season at Vicente Calderon after agreeing a loan move on Wednesday.
Cani's change of club came as something of a shock given he has started only five Liga matches this season.
And the former Real Zaragoza man has conceded he was as surprised as anyone when the opportunity to join the Spanish champions came up.
"When Atleti calls, everything else is left to the side," said Cani as he was presented by his new club on Friday.
"I was not expecting this great opportunity that I've had.
"I've been with this club for a short time and you can see its greatness right away. That is why the team is doing so well.
"I am very moved and happy. When this opportunity came, for me it was a challenge and I come to help achieve the objectives."
Cani could make his Atleti debut at Camp Nou on Sunday when Diego Simeone's men take on Barcelona.
