Rudy joined the Bundesliga champions on a free transfer, signing a three-year contract, while Sule joins on a five-year deal for an undisclosed transfer fee. However, the Germany international duo will not move to the Allianz Arena until July 2017.
Centre-back Sule, 21, who joined Hoffenheim's youth system in 2010, was reportedly the subject of a bid from Chelsea, and has started and finished all but two games for his side this season.
Rudy, on the other hand, moved to Hoffenheim in 2010 from Stuttgart and captained the side from the centre of midfield this season.
"FC Bayern have completed the signings of Niklas Süle (21) and Sebastian Rudy (26) from TSG 1899 Hoffenheim," a statement on Bayern's website read. "The two Germany internationals will join the German record champions on 1 July 2017."
Karl-Heinz Rummenigge, the club's chairman, said he is delighted to bring the duo to Munich: "We are very pleased and happy that Niklas Sule and Sebastian Rudy come to Bayern.
"The transfer of two players of the German national team is an investment in the future of the club. Sebastian Rudy comes for free. For the transfer of Niklas Sule we have found a fair and serious solution with TSG Hoffenheim."
Rudy spoke of his elation at moving to Bavaria, saying: "It is an absolute dream for me to go to Munich. FC Bayern is one of the greatest clubs in the world," he said, while Sule added: "In terms of it being a farewell I feel a little wistful too, but I can mature further with one of the best teams in the world."
Bayern sit at the top of the Bundesliga before the season resumes, three points clear of clearest rivals Rasenball Leipzig whom they beat 3-0 in the final game of 2016. The German top flight resumes on Friday when Carlo Ancelotti’s men take on Freiburg, who are currently ninth.