Assombalonga, 23, had three years remaining on the deal he signed on joining from Peterborough in 2014.
Forest owner Fawaz Al-Hasawi said he had turned down an offer from Premier League side Norwich for the forward.
Assombalonga, who missed much of the 2015-16 season with a serious knee injury, has scored 19 goals in 39 games for Championship side Forest.
His three goals this season have helped the club to seventh place after five games.
Meanwhile, Al Hasawi has said that the £13m received from the sale of Oliver Burke to German club RB Leipzig will be reinvested into the club.
"The money remains in the club, we could spend it in January or on a facility within the club," Al Hasawi told BBC Radio Nottingham.
"We are willing to reinvest it but I cannot go and get three or four players for the club. That is the manager's decision.
"We have to let him choose the right players for himself and respect that."
Winger Burke, 19, had netted four times in seven appearances this season and, despite his future potential, no sell-on clause was included in the Scot's transfer deal.
Al-Hasawi continued: "There is no sell-on clause for Burke as at first they offered £8m and I turned them down, then they offered £10m and I said 'no'.
"When they said £13m and we will pay it in one go without a sell-on clause, I said 'OK'.
"The money we got from the sale is good for the club, especially as they paid the money in one go. It's good business."
Nottingham Forest striker Britt Assombalonga has signed a new five-year contract.