The Albania international's future has been one of the headline stories on transfer deadline day, with both Fulham and Wolverhampton Wanderers battling to prise him away from Stamford Bridge.
Wolves are said to have had an approach for Broja rebuffed earlier in the month, and Chelsea were after an extortionate £50m to let the 22-year-old depart on a permanent deal in the last knockings of the window.
With neither Fulham nor Wolves bowing to those demands, Chelsea made Broja available for loan, and the two interested parties have been working tooth and nail to find an agreement with Chelsea.
According to The Athletic, a breakthrough in negotiations has finally been made, and Broja will spend the remainder of the campaign with Marco Silva's side at Craven Cottage.
The deal to send Broja across West London could reportedly pocket Chelsea as much as £4m, which will depend on appearances and also how well the striker performs in front of goal.
Wolves are now believed to have conceded defeat in their efforts to bring Broja to Molineux, while Italian giants AC Milan were also keeping tabs on the situation before Fulham shook hands with Chelsea.
Broja is expected to complete his medical in the coming hours ahead of linking up with Silva's side, who have struggled for a consistent attacking output since the summer exit of Aleksandar Mitrovic to Al-Hilal.
Former Wolves talisman Raul Jimenez has managed just five goals from 24 matches in his debut Fulham season, and the Mexico international is now facing weeks on the sidelines with a thigh injury.
Rodrigo Muniz and Carlos Vinicius represent alternative attacking options, but Broja will ostensibly slot straight into Silva's XI at the tip of his 4-2-3-1 system, assuming that there are no late complications with the Albanian's medical.
Broja has scored two goals and provided two assists in 19 matches for Chelsea in all competitions since the start of the season, having missed the first few weeks of the campaign due to the cruciate ligament tear he sustained during the 2022 World Cup break.
Since recovering from that devastating injury, Broja has only earned six Premier League starts under Mauricio Pochettino, but he still possesses a long-running contract at Stamford Bridge until 2028.
In total, the Slough-born striker has registered three goals and three assists in 38 senior appearances for the Blues, whom he has represented since 2009, but he has also been loaned out to Vitesse and Southampton over the past couple of years.
Having lost out on Wolves' signature to their West London rivals, Wolves - who allowed Sasa Kalajdzic to join Eintracht Frankfurt on loan in January - are not expected to add to their attacking ranks before the 11pm deadline.
Should Fulham register Broja's arrival before 12pm on Friday, the Albania international will be eligible to make his Cottagers debut away to Burnley on Saturday afternoon.