The 23-year-old has signed a five-and-a-half year deal at St. James' Park and joins for a reported £12million fee.
Shelvey has scored nine goals in 77 appearances for Swansea since moving to the Liberty Stadium from Liverpool for £5m in July 2013.
But his future has been in doubt since Garry Monk's departure and a move looked increasingly likely.
Shelvey told the club's official website: "I'm very excited to be here. I'm so glad that it's finally done.
"I drove up through the night to be here so it's been a manic 24 hours but it's all been worth it to come here and play for this great club."
The Magpies' boss Steve McClaren added: "I'm delighted to welcome Jonjo to Newcastle United.
"He has great experience for a young English central midfielder and is a current England international, so I'm certain he will be a great addition to the squad.
"He is a player we have admired for some time and we're very pleased that we've now been able to bring him here."
Shelvey came through the academy at Charlton Athletic before joining Liverpool in 2010. He was loaned out to Blackpool a year late and he spent three years at Anfield before moving to Wales.
He is an England international and is Newcastle's second addition in 24 hours, having club completed the signing of Henri Saivet from Bordeaux on Monday.
The duo will be presented on the pitch before tonight's home match with Manchester United.
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Source: talksport
