The 58-year-old will replace fellow Portuguese Paulo Fonseca, who Roma announced earlier on Tuesday would leave at the end of the current season.
Mourinho, sacked by Tottenham on 19 April, has signed a three-year deal with the three-time Serie A winners.
“The incredible passion of the Roma fans convinced me to accept the job and I cannot wait to start next season,” said Mourinho.
“Thank you to the Friedkin family for choosing me to lead this great club. After meetings with the ownership and Tiago Pinto, I immediately understood the full extent of their ambitions.
“It is the same ambition and drive that has always motivated me and together we want to build a winning project,” added Mourinho, who has also managed Inter Milan, Chelsea, Manchester United and Real Madrid outside his homeland.
Mourinho was dismissed after 17 months in charge of Spurs following a poor second half of the season in which the north London club slipped from top of the table to outside the European places.
This season Mourinho suffered 10 league defeats in a single campaign for the first time in his managerial career.
Mourinho’s previous stint in Italian football was a successful one with Inter Milan that produced four major honours in two years.
He won the Italian title twice, the second victory forming part of the club’s historic treble in 2009-10 which also saw them claim the Champions League and Coppa Italia.
“When Jose became available, we immediately jumped at the chance to speak with one of the greatest managers of all time,” said Pinto, general manager of Roma, who are seventh in Serie A.
“We were blown away by Jose’s desire to win and his passion for the game: no matter how many trophies he has won, his primary focus is always on the next one. He possesses the knowledge, experience and leadership to compete at all levels.
“We are supremely confident Jose will be the perfect coach for our project, for both our immediate and long-term future.”
Jose Mourinho’s managerial honours
Club Major trophies
Porto (2002-04) Primeira Liga (x2), Champions League, Uefa Cup (now Europa League), Portuguese Cup
Chelsea (2004-07 and 2013-15) Premier League (x3), FA Cup, League Cup (x3)
Inter Milan (2008-10) Serie A (x2), Champions League, Coppa Italia
Real Madrid (2010-13) La Liga, Copa del Rey
Manchester United (2016-18) Europa League, League Cup
Tottenham (2019-21) None