The Peru international's previous contract had been set to expire this summer and the striker had been expected to leave the Allianz Arena.
However, Pizarro penned a one-year extension on Tuesday, much to the relief of Guardiola, who believes that the 35-year-old attacker still has much to offer the German champions.
"It was the desire of both myself and the club to keep Claudio," the Bayern boss told FCB.tv.
"I am very, very happy because he is a special player with a lot of experience.
"Claudio knows the Bundesliga inside out, is a great guy and has great quality.
"In the last two or three months, he played outstandingly well."
Reflecting on his first season in charge, Guardiola argued that his players deserve great credit for retaining their hunger after winning a treble under previous boss Jupp Heynckes.
"It was not an easy season, especially mentally," the former Spain international said of Bayern's double-winning campaign.
"If you have won everything that you want as a player, it can sometimes be difficult to continue giving everything the following season.
"To focus each week on a football game is difficult. So, I am very proud of my players."
Guardiola also revealed that he is considering travelling to Brazil for this summer's World Cup to cheer on some of his charges.
"I hope my players can enjoy this experience," the ex-Barca boss enthused. "Maybe I'll watch a game or two on the ground."