Bayern shared footage on their social media accounts of Sane being put through his paces on Monday, the winger working out alongside new team-mate Niklas Sule.
The Germany international joined the Bundesliga champions from Manchester City in a deal worth €60million this month, signing a five-year contract to seal a return to his homeland.
"It was very good," Sane said during the short video.
"It was a small group for training with Niklas Sule, but it was great to be out on the pitch again, completing my first session here on the training ground.
"I'm just overjoyed to be here."
Sane was seemingly set to move to Bayern last year, only to suffer a serious knee injury during the Community Shield against Liverpool.
The 24-year-old played just 11 minutes in the Premier League for City this season, with Pep Guardiola revealing the Premier League club had failed in their attempts to convince the player to sign a new contract.
Bayern have already confirmed Sane will wear the number 10 shirt next season, as donned by Philippe Coutinho during his season-long loan from Barcelona.