The 23-year-old arrived at the Gunners' Hale End academy from Reading in the summer of 2015 and previously spent the 2019-20 campaign on loan at Bochum.
Osei-Tutu's contract in North London was due to expire in 12 months' time, and he failed to make a single senior appearance for the club under Arsene Wenger, Unai Emery or Mikel Arteta.
Osei-Tutu did make the bench for Arsenal in the Premier League, Europa League, EFL Cup and FA Cup, while he scored two goals and provided two assists in 30 games for the club's Under-23s.
The 2021-22 season saw the right-back make four appearances for Nottingham Forest in a short loan spell before joining Rotherham United in January, where he played 16 games in all tournaments and scored one goal in the final of the EFL Trophy against Sutton United, which came in the sixth minute of second-half injury time to level the scores.
"We wish Jordi all the best for his future with VfL Bochum, he will always be a valued part of the Arsenal family," Arsenal said in a statement.
Osei-Tutu previously registered five goals and three assists in 21 2. Bundesliga matches for Bochum and was also sent out on loan to Cardiff City during his time at Arsenal.
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