Earlier this week, the Spaniard signed a short-term deal at Stamford Bridge in order to be with the team until the season ends, with his previous deal due to expire at the end of June.
However, before that short extension was finalised, he had already agreed on a move to the Italian giants for the 2020/21 campaign.
However, in 2019/20 he has seen his playing time reduced under new coach Frank Lampard, with him having made just nine appearances in the league.
It was never likely that he would sign another long-term deal, while Chelsea have been busy signing replacements in the form of Hakim Ziyech of Ajax and Timo Werner of RB Leipzig, with more players set to follow.
With regards to the shorter-term extensions, Pedro joins the likes of Olivier Giroud, Willy Cabellero, and Willian in staying with the club until the current campaign finishes.