The former Beatles musician popped the question to the American businesswoman nearly four years after they first met in The Hamptons area of New York State during the summer of 2007.
A source told website People.com: "Nancy and Paul are getting married. Ring and all - very exciting."
Another friend of the couple added: "They have the right chemistry. They're both cool, chilled out and optimistic."
The couple have remained tight-lipped about their relationship, although in December last year it was said they were making secret preparations to marry.
A source said at the time: "Paul and Nancy's relationship is rock solid and there's no mad hurry for a wedding. Neither of them want a big deal made out of it.
"It's almost certainly going to be done very discreetly over in the US and Paul would ideally like to do it without any publicity beforehand."
The wedding will be 'Yesterday' hitmaker Paul's third, after he was married to Linda Mccartney from 1969 until her death from breast cancer in 1998 and then to former model Heather Mills from 2002. Although he didn't officially divorce Heather until 2008, they separated in 2006.
Nancy - who is the vice president of a family-owned transportation conglomerate - has been married once before, to Bruce Blakeman.
The 51-year-old businesswoman is also said to have been a big hit with the 'Drive my Car' singer's five children, Heather, 48, Mary, 41, Stella, 39, James, 33, and Beatrice, seven.
Paul, 68, and Nancy were last spotted together on Tuesday (03.05.11), when they stepped out for the Costume Institute Gala at the Metropolitan Museum Of Art in New York City.