The 28-year-old joins the Blues in a deal that could rise to £21.4million.
Pedro appeared to be on his way to Manchester United, but the move to Old Trafford fell through.
“I am very happy to be here,” Pedro told the Blues’ official website. “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.”
Very happy, I’m already Blue! Thank U all and specially @FCBarcelona for make possible to reach this point @ChelseaFC pic.twitter.com/fgERbDXLcJ
— Pedro Rodríguez (@_Pedro17_) August 20, 2015
A Barcelona statement read: “FC Barcelona and Chelsea FC have reached an agreement for the transfer of Pedro Rodriguez for 30 million euros, 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.”