Davies, who has been injured this whole campaign, has pulled on the Fulham shirt for the last time, while Karagounis will play a part in his final Fulham game on Sunday, against Swansea City.
It brings to an end the love affair between two popular players and the fans, with Karagounis famed for his sheer endeavour and Davies loved for his devotion to Fulham over six, fantastic seasons.
Speaking of Karagounis, manager Martin Jol said: "It is most likely that Sunday will be the last game that Giorgos will play for Fulham.
"He's had a terrific year and the Premier league was a great experience. There would be options for him to stay in England and would consider any challenges that may be available. It's very good that the fans of Fulham have recognised his contributions this season to vote him as the second best player and he will always have them in his heart."
"I don't want to comment on any further details about discussions with Fulham but the bottom line is that he will move on."
It brings the Greek's Craven Cottage stay to an abrupt end but, in only one year, he has left an indelible mark on the club. His work rate was unmatched across the midfield, despite his advancing years, and he was more aware than most if what this football club means to the fans.
As for Davies, Jol was keen to stress the club's support for the Welshman in what has been a difficult time, given the 33 year-old's spate of injuries.
"The thing with Simon is as long as I was here he was never fully-fit for more than two or three weeks, and that's a problem," the Ducthman said.
"When he was fit he was a wonderful player but if he's not fit we've got a problem, so we've got to sit down with him and talk about it.
"We will look after Simon and, of course, he can stay here as long as he needs to get fit, but it's about him as well. He has to make his mind up about his own fitness and if he wants to play again."
Davies, too, has left an imprint on the club that will be hard to forget. Having signed in 2007, he was a key member in our survival in 2008 and our dramatic run to the Europa League final in 2010. He scored our only goal against Atletico Madrid in that very final.