The 67-year-old Italian was sacked by Fulham last week after just three wins from 17 games in charge.
Roma have confirmed that Claudio Ranieri has been appointed as head coach following Eusebio Di Francesco's dismissal.
"I wish Roma a lot of success in the future", said Monchi in a statement released by the club.
"When Roma calls you, you can't say no", said Ranieri after his arrival was made official.
Ranieri's first match in charge will be against relegation-threatened Empoli on Monday.
"I would like to thank president [James] Pallotta, the club's management, staff, players and fans for their support during my time at the club". "We have one objective remaining this season and that is to finish in the highest possible league position and secure qualification for the Champions League. Claudio ticks all of those boxes and he's very excited to take on this challenge", said Pallotta.
The top four from Serie A qualify for next season's Champions League.
The Premier League-winning former Leicester City manager was sacked by Fulham in February, with the club 19th in the Premier League. "We have 12 games left and we need to win as many of them as possible".
During his first year, the club were genuine title challengers but surrendered Serie A, and the Italian Cup final to Inter Milan, who eventually won the treble that year.
Earlier in the day Roma announced that their sporting director Monchi had left the club by mutual agreement.
Roma are now fifth in the table, three points behind fourth-placed Inter Milan in the race to qualify for next season's Champions League.