Osei-Tutu, who spent the second half of the 2021/22 season on loan at Rotherham United, made 16 appearances in all competitions for the Millers as they secured promotion to League One, scoring once.
The versatile defender played for Bochum on loan from the Gunners in the 2019/20 season.
The full-back is close to returning to Bochum on a permanent basis this summer, with his medical already completed, according to German outlet RevierSport.
Osei-Tutu failed to force himself into Mikel Arteta’s plans for next season and had he stayed at the Emirates Stadium, he would have been included as part of the Under-23 squad.
It is claimed that the Gunners have decided to forego a transfer fee for the defender, who was under contract with them until the summer of 2023.
Bochum managed to secure their top flight status for another season after returning to the Bundesliga in 2021 by finishing in 13th place.
Die Unabsteigbaren are set to welcome back a player who scored five goals and recorded three assists for them in 21 2. Bundesliga appearances during his last stint in Germany.