The 41-year-old retired from playing at the end of the 2019-2020 season, following his fourth spell with Werder Bremen, and has been appointed as a Bayern ambassador.
Striker Pizarro spent nine seasons with Bayern across two stints, firstly from 2001 to 2007 and later from 2012 to 2015, netting 125 goals in 327 appearances.
Bayern said his new roving role will focus on promoting the club's "name, traditions and values throughout the world", as well as playing for the FC Bayern Legends team in exhibition games.
The six-time Bundesliga winner joins former team-mates Giovane Elber and Bixente Lizarazu in the ranks of Bayern ambassadors, the Champions League winner said on its website.
Pizarro said: "It is a dream to be back in Munich. FC Bayern is always described as a family, and that's exactly how it feels. Now, in my new role, I will once more give everything for this club - just like I used to as a player."
Bayern board member Andreas Jung said of Pizarro: "His South American soul has been spiced with a pinch of Bavarian through his many years in Munich, and all this, in addition to his great success as a player, makes him a perfect representative for FC Bayern."
In all, Pizarro won 16 trophies as a Bayern player, including a treble in the 2012-2013 campaign.