The Austria forward has joined Bayern Munich on a four-year contract
Sabitzer revealed he has been a long fan of Bayern and will do everything possible to help the club achieve their goals.
"As a child my Bayern jersey was my pride and joy - I got a new one at Christmas every year," said Sabitzer, who was linked with Tottenham and Arsenal.
"I'll give everything for this club."
He added: "I want to win as many matches as possible and of course collect lots of titles."
Spending seven years at Leipzig, Sabitzer helped the side to become a formidable force after their promotion to the top flight in 2016.
Sabitzer follows the footsteps of Julian Nagelsmann and Dayot Upamecano who all joined Bayern Munich from RB Leipzig this season.
The 27-year-old assisted in the side's journey to German Cup final, losing 4-1 to Borussia Dortmund and finishing 2nd in the league log last season.
The former Rapid Wien player becomes Bayern's third summer signing, coming hot on the heels of Umar Richards from Reading and Sven Ulreich from Hamburg.
Sabitzer is expected to feature for Bayern after the international break.
The Bavarians have amassed for themselves seven points in three games of the season and are currently sitting third on the table.
Sabitzer played 229 times for Leipzig as he will wear the number 18 shirt at the Allianz Arena.
Bayern CEO Oliver Kahn after completing the signing of the player said;
"Sabitzer brings everything to the table a player needs to play for FC Bayern. He will also not need a long acclimatization period because he is already very familiar with the philosophy of our coach Nagelsmann."
Hasan Salihamidzic, sporting director of the club also, added;
"We are very happy that we could win over Sabitzer for FC Bayern.
"Marcel is a very good footballer, he has a great mentality, is very ambitious and, as captain of RB, has carried responsibility on and off the pitch. After all, our coach knows him very well, also as a leadership player. We are looking forward to him."
