The Bundesliga champions had been heavily linked with centre-back Benatia after Javi Martinez suffered a serious knee injury in their DFL Supercup defeat to Borussia Dortmund.
And Bayern announced on Wednesday that the 27-year-old Morocco international has put pen to paper on a long-term deal at the Allianz Arena after they agreed a fee thought to be in the region of €30 million with Roma.
Speculation over Benatia's future had been rife throughout the transfer window, with Manchester United, Manchester City and Chelsea all rumoured to be interested in him.
However, Bayern's need for another defensive option following Martinez's injury - which is expected to keep him out for the majority of the season - has led to him moving to Bavaria.
Benatia joined Roma from Udinese in July last year and enjoyed an outstanding campaign in the Italian capital, making 33 Serie A appearances as Rudi Garcia's side finished second behind Juventus.
