Several Premier League clubs were linked with the 22-year-old, but it appears the Cottagers have won the transfer race.
Wolverhampton Wanderers had a loan bid rejected for the centre-forward before they turned their attention to Corinthians forward Yuri Alberto.
West Ham United also emerged as a possible destination for the Albania international, with Michail Antonio sidelined with a knee injury.
Chelsea reportedly wanted a £5m loan fee for letting their player leave on deadline day, but it looks like they have ultimately settled for £4m.
Broja came through the Blues academy and has made 38 appearances in all competitions, bagging three goals and three assists.
A serious injury kept him outside for around nine months before he returned to the first team in September.
The centre-forward has bagged two goals and two assists in 19 appearances in all competitions this season.
But with Christopher Nkunku and Nicolas Jackson also available, the Premier League giants decided to offload the Albanian.
Chelsea reportedly only wanted a loan with an obligation or a permanent transfer worth over £35m.
But they later became flexible and were prepared to consider a straight loan.
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