The fee for the 28-year-old is more than £21 million.
The Barclays Premier League champions stepped in to sign the Spain international after Manchester United withdrew their interest.
Chelsea announced the deal on their website before Pedro joined compatriot Cesc Fabregas in taking to the training field in Surrey.
Jose Mourinho’s side are preparing for Sunday’s game at West Brom, where Pedro could make his debut.
Pedro said on chelseafc.com: “I am very happy to be here. I am very excited to start my adventure at Chelsea and I am here to keep winning titles.
“Thanks to the club and the supporters for giving me the opportunity to put the blue shirt on.”
Pedro had been a target for United throughout the summer, with the club’s executive vice-chairman Ed Woodward flying to Catalonia on Monday in an attempt to seal a deal for the player.
But things changed rapidly on Wednesday as it emerged that Louis van Gaal had withdrawn his interest, while Chelsea were moving to steal a march on their rivals.
It was reminiscent of the deal two years ago in which Willian was on the verge of signing for Tottenham Hotspur before Chelsea swooped for the Brazilian.
Mourinho has acted quickly and decisively in the transfer market after Chelsea endured their worst start to a season in 17 years.
Shortly after their 3-0 defeat at Manchester City last Sunday, Chelsea signed left-back Baba Rahman from Augsburg for £21m, and Pedro’s arrival gives Mourinho’s side fresh attacking intent.
The Blues also hope to conclude the signing of Everton defender John Stones before the transfer window shuts on 1 September.
Barcelona confirmed the fee which they have received for Pedro was €30 million (£21.4m), with €3m (£2.14m) of that performance-related.
Barcelona said on their website: “FC Barcelona and Chelsea FC have reached an agreement for the transfer of Pedro Rodriguez for €30m, of which 3 million are dependent on performance.
“The club wishes to publicly express its gratitude to Pedro Rodriguez for his professionalism and dedication while with the club, as well as to wish him all the best in the future.”