New Barca head coach Luis Enrique has been busy reshaping his squad in the close-season and Fabregas was deemed surplus to requirements at Camp Nou.
Fabregas scored 28 goals in 96 La Liga appearances during his three-year period in Catalunya, and Pedro was saddened by the 27-year-old's move to Stamford Bridge.
"Everybody knows Cesc is a great player, one of the best in his position in the world," Pedro said.
"It's a shame for my position because obviously where I play, as a striker, he is a guy who can provide you with very good passes.
"As a friend, we've got a very good relationship and I'm going to miss him a lot.
"In terms of Chelsea being Champions League rivals of ours, they've built a very good team and with Cesc as well, they're going to be very difficult to beat."
Pedro also stated that he believes the four-month ban from all football related activity handed out to new Barca signing Luis Suarez for biting Italy's Giorgio Chiellini was overly harsh.
"I think the punishment by FIFA is excessive," he added. "But we have to leave that to one side.
"He'll be very welcome in Barcelona and the supporters will be behind him as soon as he starts playing and is giving his best for the team. I'm sure he will do well with Barca."
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