Real Madrid sold the 32-year-old Spaniard for a reported fee of £7m to the Bundesliga champions, with Sammer believing that he was just the type of player the club needed.
"We have been looking for a defensive midfielder, he is that type of player," Bayern's sporting director said, according to Sky Sports News.
"Xabi Alonso has incredible skills, passing and ball control. He has an eye for the game, he holds defending ability and he is physically strong.
"He just has to remain fit and healthy. Then we will enjoy his spell at our club."
Alonso enjoyed a five-year spell at Madrid where he won the La Liga title and the Champions League during his stint.