The deal was offered to the 18-year-old academy product in the wake of the impact he made at the end of the season when three goals in two games went a long way towards keeping the Cobblers in the Football League.
"Everyone saw the impact Ivan made at the end of the season and we were keen to tie him down to a longer deal," said manager Chris Wilder.
"We are the excited about the progress he as an individual and we as a club could make in the next three years."
Former Sixfields favourite Bayo Akinfenwa, meanwhile, has rejected the offer of a new deal at Gillingham.
***Update*** Wilder has decided not to offer Mathias Kouo-Doumbe a new contract and the 34-year-old will now leave Northampton safe in the knowledge that his goal against Oxford on the final day helped secure safety for the club.