The 24-year-old striker will cost Boro a reported £14million and that will eclipse the £12.7million fee Boro paid Heerenveen for striker flop Afonso Alves in January 2007.
Assombalonga travelled Rockcliffe Park today to hammer out the deal and he could have a medical and sign in the next 24 hours.
The deal for the striker is set to be worth an initial £14m, although this could rise depending on promotion.
Boro have seen off Premier League sides Burnley and Watford, who were both chasing the forward, who returned from Forest’s pre-season trip to Florida at the weekend.
He is believed to have been given the go ahead to hold talks with Boro after Burnley’s £8million offer last week was rejected.
The Clarets are believed to have improved that offer, but it fell way short of Boro’s bid and the former Peterborough man looks all set to join the Teessiders.