Former Arsenal star Campbell joined the Magpies in August last year but managed just eight appearances in all competitions this season whilst Kuqi was brought in as cover for the departed Andy Carroll and injured Shola Ameobi in January and played just six times.
"Sol's gone and good luck to him. He has been an icon in the game, but he didn't feature too much here," Alan Pardew told the Newcastle Chronicle.
"Our centre-backs have been a strong point for us this season and that's perhaps why. But it's good luck to Sol and we must look forward now instead."
On Kuqi, he added: "He was added to our squad and he didn't get the games he wanted.
"He was a bit frustrated at not getting on as much as he wanted because he came here to show people what he could do.
"The opportunities for him were scarce because our form during that time wasn't bad, we lost just four times in the last 14 games while he was here.
"The fans may not have seen him, but he became a bit of a legend at the training ground, he's been a warrior in training.
"He's gone, though, and I have wished him well. The sad thing is he really took to the place. He loved the people and the area.
"I can only advise teams like Hartlepool and Carlisle United to take a really good look at him this summer. He will be brilliant for them if he got the chance."