"The club have agreed a deal in principle with West Ham United to sign goalkeeper Darren Randolph, subject to a medical and personal terms", read a statement on Middlesbrough's official website.
Joe Hart's recent arrival at West Ham left Randolph and Adrian fighting for the role of second-choice keeper, while Boro are short in the department after losing Brad Guzan and Victor Valdes.
"The Republic of Ireland worldwide will travel to Rockliffe Park on Saturday in anticipation of finalising the move".
The Wicklow native - capped 21 times for Ireland - has been at West Ham since 2015 and established himself as first choice under current manager Slaven Bilic for a period.
He made 22 Premier League appearances in total, six more than his Spanish rival as the Irons finished their campaign in 11th place.
Randolph is set to be Teeside boss Garry Monk's sixth new signing after clinching the signatures of Jonny Howson, Cyrus Christie, Martin Braithwaite, Connor Roberts (loan), and Britt Assombalonga.