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 champions.
"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.