According to Greek source Gazzetta.gr, the deal was struck before PAOK’s shock Champions League win over Benfica on Tuesday.
Akpom, 24, told PAOK that he wanted to return to England, where he was a youth product at Arsenal.
Middlesbrough will pay €3m and PAOK will also receive a percentage of any future transfer fee.
Unless of any unexpected twists, the former England under-21 international will soon join Neil Warnock’s side.
Akpom moved to the Greek giants in in 2018 and has gone on to score 18 goals in 79 appearances.
He has been an active part of PAOK’s Champions League qualifiers, assisting the only goal in their win over Besiktas and playing 70 minutes in their 2-1 win over Benfica last night.
Sky Sports claimed in July that Besiktas had agreed a €2m fee with PAOK for Akpom.
However, the striker will continue his career back in England with Middlesbrough.
Akpom’s return to England has now been made official by Middlesbrough.
— Middlesbrough FC (@Boro) September 19, 2020