The Uruguay striker was hit with the suspension after his infamous lunge at Italy striker Giorgio Chiellini during the recent World Cup.
Barca were still happy to spend around £75million to buy the forward from Liverpool despite his enforced sidelining and the forward, whose initial appeal was rejected, is taking his case to the Court of Arbitration For Sport.
Pedro is looking forward to linking up with the controversial striker and believes he has been harshly treated.
"I think the punishment by FIFA is excessive," he said during Barca's week-long training camp at St George's Park, near Burton.
"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."
Pedro also lamented the sale of friend and colleague Cesc Fabregas to Chelsea earlier this summer.
"Everybody knows Cesc is a great player, one of the best in his position in the world," said the Tenerife-born forward.
"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."