The 34-year-old Spain international had arthroscopic surgery and was ruled out for the final weeks of the season, meaning he missed the nation's triumphant Euro 2012 campaign in Poland and Ukraine.
"The captain trained apart from the rest of the squad in the group's penultimate session before they fly out to Germany on Tuesday for their first pre-season friendly against Hamburg," Barca said in a statement on their website (www.fcbarcelona.com).
"Puyol will undergo further medical tests next Monday, July 30th, to confirm his fitness to return to full training - the same day that the team's Spanish internationals resume training," the statement said.
Puyol's team mate Dani Alves added at a post-training news conference: "I am very happy that Puyi is back, that's he's in good shape and he is recovering.
"I think that with Puyi you don't need to look at his age, because it's irrelevant. For me, he's like a two-year-old kid."