The former Ghana international wants to draw near to his family in Germany after 18 months at the Farum-based side.
"Otto has helped the team in diverse ways with his immeasurable contribution and we have been delighted to have him as part of the staff.
"We understand that Otto wants to get home to his family in Hamburg, where his wife and three children live," Jensen said.
Addo who won the German league with Dortmund in 2002, thanked the club and the staff for their support during his stay since January 2016.
"It has been a fantastic experience and I leave here (FC Nordsjælland) with loads of experience. I have learned a lot from my colleagues," he said.