Bamford is set to complete his move to 60 miles south to Elland Road in the next 48 hours, reports the Yorkshire Evening Post.
Leeds have been looking to add a striker to their squad after struggling last season upfront and so far the summer transfer window has been a disappointment for the Whites, with failed attempts for Hull’s Abel Hernandez and Derby’s Matej Vydra.
Leeds boss Marcelo Bielsa has made the acquisition of a proven Championship striker a priority this summer and the deal for Bamford has progressed quickly over the weekend.
Bamford is expected to have his medical on Monday before completing a move which could worth £10m, after a number of add-ons are included in the transfer.
The 24-year-old scored 13 goals in 44 appearances for Middlesbrough last season helping the club secure a play-off spot.
Middlesbrough paid Chelsea £6million to sign Bamford on a permanent deal in January 2017.
Leeds’ capture of Bamford is expected to end their interest in Vydra, after the Czech striker reported demanded more than £50,000 a week in wages.
Bamford will become Leeds’ second permanent signing of the summer after the club completed the transfer of Wolves defender Barry Douglas on a three-year deal on Saturday.
The Whites have also brought in midfielder Lewis Baker and goalkeeper Jamal Blackman on season-long loan deals from Chelsea.