Teesside-raised Bevington, a former managing director of Club England with the Football Association, has been working in his role for the past 18 months.
Boro have issued a statement but are refusing to comment further on the matter at this stage.
A club statement read: “Middlesbrough can confirm that head of recruitment operations Adrian Bevington will part company with the club at the end of the month.”
Bevington added: “It has been a pleasure to work with (chairman) Steve Gibson, (chief executive officer) Neil Bausor and everyone at the club. I would like to wish Jonathan Woodgate, his staff, the players and supporters every success in the future.”
CEO Bausor continued: “On behalf of everyone at the club I would like to thank Adrian for his work over the past 18 months and wish him well for the future.”
Meanwhile, Woodgate has confirmed that top-scorer Britt Assombalonga (ankle) remains a doubt for the game with Huddersfield Town on Boxing Day.
The £15m striker has missed the club’s last two matches.
The Boro chief said: “We have Anfernee Dijksteel, George Friend, Darren Randolph and Ryan Shotton out and Britt is only 50-50, as well as having Paddy McNair and Marcus Browne suspended. Hopefully there will be nothing new,”