Morata, 27, landed in Turin on Monday to finalise his move to re-join the Italian champions.
Morata described the move to Juventus as a "story of great love" in a post on his Instagram page.
"To have played at Atletico has been one of the best things that has happened in my life," he added. "Those that know me know that I always will have my membership in the Metropolitano. I want to say thank you for the incredible two years in which I've experienced unforgettable moments and felt as part of the group from the moment I arrived. To have defended these colours gives me pride and to have celebrated goals with this jersey is a dream come true."
The agreement gives Juventus the right to definitively sign Morata by the end of the 2020-21 season for a transfer fee of €45 million, which would be payable over three years. Juventus also have the right to extend the contract on a temporary basis until the end of the 2021-22 season for a fee of €10m.
The striker enjoyed a successful loan spell at Juve between 2014 and 2016 where he scored 27 goals, including a strike in the 3-1 defeat against Barcelona in the 2015 Champions League final.
The Spain international won two Serie A titles and two Coppa Italia trophies in his two-year stint at the club.
"[He] is isolating at home, following the health authorities' guidelines," a club statement said.
"Following the result, the La Liga protocol has been activated and our players will complete the next training session individually."
Atletico begin their La Liga season at home to Granada on Sunday.
"As many of you know, I had a COVID test done yesterday and it came out positive," he said. "I feel fine but I have lost my sense of smell and taste.
"Please let's look after one another. I was one of those people who never thought I would get it. Now I'm isolating and following the protocol in order to return stronger than before."
Gimenez is just one of six players to have tested positive since the pandemic started. Atletico coach Diego Simeone tested positive on Sept. 12 and is still in quarantine.
ESPN's Adriana Garcia contributed to this report.