The 20 year old son of former City Reserve boss Alan Cork has joined on loan until the end of December.
The midfielder who can play in defence has been on loan at Bournemouth, Scunthorpe where he scored twice against City, Southampton and Watford.
City are waiting to hear back from the Football League and FA Premier League to see if he can play against Swansea tomorrow.
Chris Coleman said to the club website: "This is another excellent addition to the squad and Jack is the second promising young Chelsea player to join our ranks this season.
"He is very highly-regarded at Stamford Bridge and he has already played close to 100 matches while on loan with other Football League clubs so has good experience for his age.
"We made a substantial offer for Jack earlier in pre-season to bring him to the club permanently but Chelsea did not want to sell which shows how much they think of him - and how highly we consider him.
"That said, we are delighted that they have let him come out on loan to us and this is further sign of what we are trying to achieve at the club.
"We are still hoping to make further additions before the transfer window closes and a lot of work is going on behind the scenes to make that happen."
"That said, we are delighted that they have let him come out on loan to us and this is further sign of what we are trying to achieve at the club.
"We are still hoping to make further additions before the transfer window closes and a lot of work is going on behind the scenes to make that happen."