The 33 year old had been on the fringes of the first team at the Liberty Stadium and has made just 2 league appearances under Brendan Rodgers.
It was revealed last night by a Derby spokesman that one of their targets had become available over the weekend, and that a deal was close.
Kuqi scored 7 goals in 24 appearances for the Swans and goes straight into the Derby squad to face Hull City tomorrow evening.
The move leaves Swansea even lighter in the forward ranks with just Stephen Dobbie the only fully fit striker ahead of the visit of Coventry City.
"Shefki has been a potent threat against us in the past, and now we hope he can do exactly the same in a Derby County shirt," said Rams boss Nigel Clough.
"He will give us a presence in attack; he is big, strong and has been a goalscorer wherever he has been."
Rodgers said that the move would help to free up a space in the squad for new additions: "Shefki hasn't figured a great deal this season and we both felt that the move would be a good chance for him to play some games.
"We had an open conversation about it. He's a good guy and I respect that at the stage of his career, at 33, he wants to play games, which is understandable, and we wish him well at Derby.
"Shefki's a great professional, but his strengths are different to the type of game we play here.
"It also gives me the chance to use the space to bring someone else in.''
