The midfielder, who is a free agent, is set to sign a three-year deal once a medical is completed.
Tottenham also lodged an interest in Eriksen but after Antonio Conte stepped back from a deal, United were able to swoop in.
His contract at Inter Milan was officially terminated in December 2021 and he signed from Brentford as a free agent in January 2022.
He was instrumental in helping Brentford finish 13th in the Premier League in their first season in the top flight following promotion from the Championship with his fine form ensuring interest from a host of clubs across Europe.
United have won the race for his signature and he will be part of Ten Hag’s new era at Old Trafford.