Erik Nevland is undergoing a medical at Craven Cottage after Fulham's latest offer was accepted by Groningen.
The Dutch club had already rejected two bids from the Premier League strugglers before further talks on Sunday evening brought about an agreement.
Fulham have agreed to pay 2.5million euros (£1.85million) up front, with an additional 500,000 euros (£370,000) to be paid, if the club avoid relegation.
Groningen's general manager Hans Nijland told the club's official website: "When he asked us not to deprive him of the opportunity of his life, out of the respect we have for him, we negotiated with Fulham.
"Initially, the difference between the demands and the offer was too far from each other and the case seemed to be closed.
"Last weekend, Fulham again contacted us and that led to an agreement."
Fulham boss Roy Hodgson is confident that the Norwegian striker, who he worked with at Viking, will be a valuable addition to his squad.
Hodgson told VG: "He is having the medical right now.
"He is a particularly good striker and that's one of the reasons why Sir Alex Ferguson brought him to Manchester United 10 years ago.
"He plays with his heart outside his shirt and that is the type of player we need right now."