The Blues centre-back has been used sparingly by Maurizio Sarri this season and is set for a new challenge with the Cottagers.
And the transfer has resulted in Fulham terminating the loan deal for Manchester United defender Tim Fosu-Mensah.
That’s according to Love Sport who claim the 21-year-old has been let go to free up space in their squad.
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Chelsea have preferred the partnership of Antonio Rudiger and David Luiz this season with Andreas Christensen providing backup.
Arsenal were also interested in the services of Cahill, but it looks like Fulham have beaten them to his signature.
Sarri praised Cahill last month but admitted he could leave Stamford Bridge.
“I respect him very much because he has won everything with this club,” he explained.
“I have to do my job. Every match, I have to choose. For me, he is not able to [be] on the bench.
“Maybe he is the best in the box, but our defenders may play 100 or 110 balls in a match so I need very technical defenders.
“It is not my decision, but it is up to him and the club.
“He is in the last year of the contract.
“He has to decide for a new contract here or another club.
“For the over 30 [players] the club usually offers only one-year contracts.
“If he has an offer of three years, he can of course choose something [a transfer away from Chelsea].”
Chelsea return to action against Nottingham Forest in the FA Cup third round on Saturday (3pm).
The Blues were booed off by their own fans last night as they drew 0-0 with Southampton in the Premier League.