The Uruguay international, part of his country’s Copa America squad this summer, has been given permission to have a medical and talk terms with the Championship club.
An Espanyol statement read: “The Uruguay striker will join Middlesbrough once he passes a medical and signs his contract with the English club.
“In the next few days, Stuani will no longer be an Espanyol player as a preliminary agreement exists for the player to leave our club. The intention of the forward is to join Middlesbrough, coached by Spanish manager Aitor Karanka.
“The Uruguay international was expected to join our team in training this week but the player has been given permission not to do so in order to aid his transfer to his new team.
“The player’s wish is to say goodbye to his team-mates next week in Barcelona before joining his new club.”
Stuani scored 16 goals in all competitions last season as Espanyol finished 10th in La Liga.