Pedro wants to win trophies at Chelsea after being convinced to move to the Premier League champions by Jose Mourinho and Cesc Fabregas.
The 28-year-old on Thursday signed a four-year deal after the Blues agreed a £21.4million (30 million euros) fee with Barcelona, with £2.1million of the payment being performance-related add-ons.
The Spain winger, who had been a target of Manchester United, immediately trained with his new team-mates at Chelsea's Cobham training ground and could make his debut in Sunday's match at West Brom.
It was Mourinho and former Barcelona playmaker Fabregas, whose first season at Stamford Bridge ended with a Premier League and Capital One Cup double, who persuaded Pedro to join the Blues.
Pedro said on chelseafc.com: "He (Mourinho) is one of the main reasons why I'm here. He phoned me a few times and said he needed me to make the team stronger.
"He has won titles wherever he has been. I am really looking forward to playing under him and hopefully winning more titles.
"I spoke to Cesc. We are very good friends. I knew I would feel at home here and that was one of the main reasons why I decided to join.
"He's a great player, he's got brilliant vision and he links up really well with the other attacking players. I know we work well together on the pitch so I can't wait to play with him again.
"I have also played with Diego Costa and Cesar Azpilicueta before, for the national team, so I feel very comfortable here."
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But things changed rapidly on Wednesday as it emerged that United boss Louis van Gaal had withdrawn his interest while Chelsea were moving to steal a march on their rivals.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 which saw Willian on the verge of signing for Tottenham 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, Chelsea signed left-back Baba Rahman from Augsburg for £21million, 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 September 1, although the Toffees are sticking firm and determined to hold on to the England international.
Pedro's arrival could have repercussions for Juan Cuadrado, who has disappointed since his January arrival from Fiorentina, or Victor Moses, who is back at Chelsea after spending last season on loan at Stoke.
Oscar and Willian are others who could find themselves in need of justifying their places, although Mourinho will be less inclined to lose the Brazilian pair.
Pedro wishes to hit the ground running and is versatile, so could provide a central attacking option, too.
"I am ready to start playing straightaway if the manager selects me," he said.
"Sometimes I play on the right, sometimes on the left, but wherever I play I will give my best.
"I am very fast. I do everything possible to win. I have helped Barcelona win titles and I want to do exactly the same thing at Chelsea, because ultimately we are all here to win things.
"It's a new challenge and I can't wait to get going."
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