The 32-year-old Spain international will leave Stamford Bridge after five seasons when the current campaign ends.
And Roma are filing the last contractual details for Pedro, who will arrive in the Italian capital in September.
Pedro has made 18 appearances in all competitions for Chelsea this season, scoring two goals.
One of the main protagonists of Pep Guardiola era Barcelona, the winger will soon continue his career in Italy.
According to recent reports, Pedro will sign a two-year deal with Roma.