The Cottagers will beat Wolves in the race to sign the 22-year-old, who will undergo a medical in west London tonight.
Chelsea are believed to have accepted offers from both clubs and allowed the Albania international to pick his favoured move.
The deal could see Chelsea earn £4million but that figure drops to a nominal amount if he plays over 50 per cent of Fulham's matches.
The Blues hope Broja can help regain form on loan at Craven Cottage, having scored just two goals 19 matches since returning from a 10-month lay-off after major knee surgery.
The Albania international will then likely be sold in the summer to help balance the books, so Chelsea can re-enter the market to sign a top-level striker, with Napoli's Victor Osimhen among the top targets.
Broja's loan spell could put him in the shop window while also being a major boost for manager Marco Silva, who lost Raul Jimenez to a suspected hamstring injury in a midweek draw with Everton.
Fulham have struggled to replace Aleksandar Mitrovic since he was sold to Al-Hilal for a club record sale last summer.
Atletico Madrid have also sounded out the conditions to sign Broja but were only weighing up a move in case one of their strikers left.
They could be suitors again by the summer, with Broja widely expected to be available for sale in the market.