The 33-year-old ended his five-year spell at the west London club earlier this month, having scored 43 goals in 206 appearances and helping Chelsea win the Premier League title in the 2016-17 season and the FA Cup the following year.
"I am delighted to be here at Roma," Pedro said in a statement. "I'm excited for this challenge and to compete to achieve our targets over the coming seasons.
"I want to thank the fans for the welcome they've given me. I hope to make them happy."
Pedro started his career with Barcelona, winning the Liga title five times and Champions League on three occasions.
He was also part of Spain's squad which won the World Cup in 2010 and the European Championship two years later.
Roma finished fifth in Serie A last season and will play in the Europa League next term.
The club was taken over by U.S billionaire Dan Friedkin earlier this month in a deal worth more than $700 million.
The new Italian season begins on Sept. 19.