According to Sky Sports Germany, Frankfurt will pay 12 million euros for the 20-year-old German, who is expected to sign a contract until 2030 in the coming days before joining the club's pre-season training camp.
The transfer follows a series of player departures Bayern have worked on in recent weeks, having already completed Alexander Nübel's exit earlier this month.
Negotiations between Bayern and Frankfurt were reportedly smooth and cordial, building on the strong relationship established when Nathaniel Brown moved from Frankfurt to Munich earlier this summer in a deal worth close to 55 million euros.
It remains unclear whether Bayern have secured a buy-back clause, matching rights, or another provision that would allow them to influence any future move involving Aseko.
The midfielder earned widespread praise during his loan spell at Hannover, impressing in the 2. Bundesliga last season. Hannover exercised their option to make the move permanent before Bayern activated a buy-back clause to bring him back to the Allianz Arena.
Earlier reports suggested Aseko could feature in Vincent Kompany's pre-season plans, with the Bayern coach expected to assess him, although other reports indicated the club would be willing to sanction a permanent sale if an appropriate offer arrived.
Bayern are not expected to enter the market for another midfielder, with the club believing it has sufficient depth through its three established options and several versatile players.
Having already spent a combined 110 million euros on Nathaniel Brown and Ismael Saibari, Bayern have largely concluded their summer business and are now focused on balancing their finances while remaining attentive to any late transfer opportunities.