Maurizio Sarri confirmed the Spain striker had asked to leave Chelsea, with the 26-year-old describing his Metropolitano move as a dream.
Former Real Madrid striker Alvaro Morata says it was always his intention to play for city rivals Atlético Madrid.
Morata was on Atlético's books as a youngster and even acted as a ball boy for the club, but it was across the capital at Madrid where he broke through as a professional footballer.
The Spain striker, who had a successful two-year spell at Juventus, joined Chelsea from Madrid in 2017 and became the Blues' club-record signing.
After making a strong start at Stamford Bridge, a back injury contributed to Morata subsequently struggling at Chelsea and he slipped down the pecking order after last week's arrival of Gonzalo Higuaín on loan from Juve.
Morata joined Atlético on an 18-month loan deal on Monday to complete his return to LaLiga, where he won titles with Madrid in 2011-12 and 2016-17.
Atlético are in the hunt for this year's LaLiga crown, with Diego Simeone's side five points back from champions Barcelona, and Morata will add to their attacking options with Diego Costa recovering from foot surgery and Nikola Kalinic having only scored twice in the league this term.
And Morata could not be happier to be given a fresh start in his home city, with his Atlético debut potentially coming at Real Betis on Sunday.
"In my career, it is a dream come true," Morata told Atlético's club website. "When I was young I saw all the Atletico legends and the other players of LaLiga.
"It's very important for me and it means a lot because I always wanted to play for Atlético Madrid - it's a very special day for me. I know Atletico: what it means, this club, this name. I already know the club inside.
"I know what I need to do here to have success and I think I'm in the right place to make another step in my life in a very important step in my career. I know a lot of team-mates and I know the club and I'm ready to fight and to play."