The Germany Under-21 international had been linked with a move to the Allianz Arena throughout the campaign, and a four-year deal was confirmed by the German and European champions on Tuesday.
Questions remain as to whether Rode - who has played 17 times in the Bundesliga for Frankfurt this season - will be able to make the step up to Bayern, who have largely been recognised as the best side in European football over the past 18 months.
He told Bild: "Many people think that only seasoned professionals can make it at Bayern Munich.
"I have to prove the opposite. I dare to do that, despite the fierce competition. I'll show everyone that I can do it.
"I have been assured in no uncertain terms that the coach is behind this transfer. There are no guarantees, I have to prove myself in training.
"If a team has been so successful, new players such as (Robert) Lewandowski and I are also important to maintain the hunger for success."
One of Rode's first priorities will be to ensure he is fully fit, as he has not featured for Frankfurt since February due to a knee injury.
