The 25-year-old, who has toured South Africa, Zimbabwe and the West Indies with the full national squad and has played One-day International cricket for England, has put pen to paper on a three-year deal at Trent Bridge.
Swann said: "Notts have enjoyed a highly successful season and have signed a number of top quality players during the past year.
"Mick Newell inidicated to me that he intends to continue to strengthen the team and the club is highly ambitous for success.
"Trent Bridge has always been one of my favourite grounds and the facilities are world class. I am really looking forward to working with Rod Marsh at the National Academy this winter and am excited by the new challenge at Trent Bridge.
"I hope this move will help in re-establishing myself in the England team through a string of top performances for Notts in Division One next summer."
Notts Director of Cricket Mick Newell added: "Graeme is a high quality off-spinner who will further strengthen the Nottinghamshire attack and our batting line-up.
"With the team having gained promotion to Division One of the Frizzell County Championship and requiring just one more win from three matches to secure promotion in the totesport League it is important to continue the strengthening of the squad that commenced last winter.
"Graeme will play a major part in all competitions next summer as he is an international class player in both limited overs and Test cricket.
"He has been selected to join Kevin Pietersen and Paul Franks at the National Academy this winter and we hope his performances with Notts next summer will build on a successful winter and put him in contention for a recall to the England team."
THURSDAY 21 SEPTEMBER 2017
ENGLAND v WEST INDIES