The 23-year-old former Liverpool player has signed a five-and-a-half year deal for an undisclosed fee, although reports suggest the sale has cost the Magpies around £12 million (16 million euros, $17.3 million).
Shelvey, who begun his senior career at Charlton Athletic, had become a peripheral figure at the Welsh side over recent weeks.
He becomes the second midfield reinforcement at Newcastle in 24 hours after Senegal international Henri Saivet arrived from Bordeaux on Monday for around £5 million.
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"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," said Shelvey, who has represented his country six times since making his debut in October 2012 against San Marino.
Newcastle manager Steve McClaren said: "I'm delighted to welcome Jonjo to Newcastle United. He has great experience for a young English central midfielder and he 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."
Newcastle are currently 18th and in the final relegation position with Swansea just one place and two points better off.
Shelvey's last appearance for the Swans was in Sunday's 3-2 FA Cup third-round defeat at fourth tier Oxford, after which he became involved in a row with a disgruntled fan as he left the pitch.
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