They had triggered the winger's €30m release clause and beat Manchester United to the 28-year-old, despite reports United had agreed terms over a move.
But it is understood Barca will not get the full figure immediately from the transfer.
Instead, they will receive £19.3m now and a further £2.1m when the player makes an agreed number of appearances.
Pedro rejected the chance to join United this week after speaking to Chelsea midfielder Cesc Fabregas about life at Stamford Bridge.
Pedro signed a four-year contract at Chelsea yesterday
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The Spain international had only recently agreed a new contract with Barca, which reduced his buy-out clause from around £100m down to the figure Chelsea will fork out.
"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," he told the club's website.
"Thanks to the club and the supporters for giving me the opportunity to put the blue shirt on."