"We're very happy Leon has chosen Bayern," said Jochen Sauer, head of the FC Bayern Campus.
"We're convinced he will make great progress at Bayern."
Dajaku scored 17 goals in 31 appearances for Stuttgart's Under-19 side last season.
He also played twice in the Bundesliga for the senior side, who were relegated after losing to Union Berlin on away goals in a play-off tie.
The hope at the Allianz Arena is that Dajaku will one day be ready to lead the line for the senior side.
As things stand, Robert Lewandowski is very much the go-to man in the final third of the field.
There has been speculation about the 30-year-old’s future again this summer, but he remains tied to a contract which still has two years left to run.
Bayern are also considering putting fresh terms in place with the Poland international, with club chairman Karl-Heinz Rummenigge confident that an agreement can be reached.
He has told Bild: "It's not all wrapped up, but there's already the development with Robert that he feels extremely comfortable with Bayern Munich.
"When you look at his body, this is a player who can easily play at this level for a few more years."
With Lewandowski expected to stick around and additions being made with one eye on the future, Rummenigge has moved to rule out a move to bring Mario Mandzukic back to the club from Juventus.
He has said of those rumours: "Nothing is planned in that direction."
Bayern are, however, in the market for another winger to help counter the departures of two iconic figures.
"We still need a winger because we lost two with Franck Ribery and Arjen Robben," said Rummenigge.
"But I don't want to promise anything because there is no point in making big promises."
Barcelona forward Ousmane Dembele, who has previously spent time in Germany with Borussia Dortmund, is among those said to be registering on Bayern’s recruitment radar, along with Manchester City star Leroy Sane.