The 24-year-old Hosogai is on loan from Bayer Leverkusen, which signed him from the J-League club Urawa Reds in December.
Hosogai said Wednesday on his website that “I will continue to play for Augsburg. It’s been officially decided.”
Augsburg secured promotion to the Bundesliga for the first time despite losing 2-1 at second division champion Hertha Berlin on Sunday.