The 67-year-old finalised a deal after arriving in the Italian capital on Friday.
He'll be aiming to lift Roma from fifth in the table and will be hoping to bring them back into contention for Champions League qualification next season, after the club were knocked out of this season's competition by Porto on Wednesday.
"I'm delighted to be coming back home".
"When Roma calls you, you can't say no", said Ranieri after his arrival was made official.
"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".
"What we need now is a safe pair of hands to guide us back into the top four and ensure that we are playing Champions League football again next season. Claudio ticks all of those boxes and he's very excited to take on this challenge", said Pallotta.
Ranieri managed Roma between 2009 and 2011, leading them to a second-place finish in Serie A and the Coppa Italia final in 2010.
A native of Rome, Ranieri won a Premier League title in 2017 as manager of Leicester City and has an extensive coaching resume with clubs from all over the world including stints with Chelsea, Monaco, Atletico, Valencia, Juventus, Parma and Nantes.
TUKO.co.ke previously reported that Roma sacked Francesco a day after the Serie A giants were bundled out of the Champions League.
Arsenal are confident Monchi will join them as technical director after he left Roma on Friday.
He then coached Nantes for a season before taking over at Fulham in November 2018, only to be sacked on February 28.