The 34-year-old joins the Magpies on a free transfer after his contract at Swansea was cancelled by mutual consent last month.
Kuqi has agreed a deal that will keep him at Newcastle until the end of the season.
“I got a phone call from my agent last week who said there might be a possibility to go there [Newcastle] and when I heard this I was over the moon,” Kuqi told Sky Sports News.
“In the beginning it was hard to believe, but in the end it all came true.
“I don’t really have the words to describe how happy I am. To get this chance is a massive thing for me.
“I am just happy to be here now and I can’t wait to start and hopefully try to do the best I can for Newcastle United.
“For me, it is a great opportunity just to be back in the Premier League again. It is something I have tasted before.
“Everybody knows it is the best league in the world and to be part of it and a club the size of Newcastle United, I am really proud. It’s an honour to be here.”