The 24-year-old moved to the Riverside Stadium following an impressive season at City Ground.
Assombalonga, who scored 14 goals last season, outstrips the £12.7m Boro paid for Brazilian striker Afonso Alves in 2008.
With this, he becomes the most expensive player in Championship history.
"I can't wait to get started and train with the boys," he told club website.
"There's a good feeling around the place. From the minute I walked in it felt right."
He becomes Garry Monk’s
Ronald Koeman's fifth signing of the summer following the arrivals of Martin Braithwaite, Jonny Howson, Cyrus Christie and Connor Roberts.
Really happy to have signed for Middlesbrough FC, it was a pleasure working for Nottingham forest fc. I would like to thank players, staff & fans at forest for everything, wishing you all the very best. On to the next step in my career, i thank god because he had a plan for me & i am thankful for the great family & friends support around me