The Swiss international has failed to make a single appearance for Celtic this calender year after falling completely out of the first-team picture under Ange Postecoglou.
The 25-year-old has joined the Europa League outfit on an initial loan deal until the end of the season. According to Kleine Zeitung, the contract also includes an option to buy for around £2.1million next summer.
The move has freed up a wage should Postecoglou look to strengthen his side with another new arrival before the transfer window closes on Thursday.
Ajeti joined Celtic in a £5million summer move from West Ham two years ago under Neil Lennon, but has dropped down the pecking order for the central striking role behind Kyogo Furuhashi and Giorgos Giakoumakis.
He scored nine times in 47 appearances for the Parkhead side.