McCartney's London based spokesman confirmed a report on People.com that the singer will wed Shevell, a New York-based businesswoman, in what will be his third marriage.
"It's true!", spokesman Stuart Bell said.
People.com quoted an unidentified source close to Shevell as saying McCartney had proposed.
"Nancy and Paul are getting married. Ring and all -- very exciting," the source told People. "They have the right chemistry. They're both cool, chilled out and optimistic," the source added.
Shevell, 51, a board member of New York's transportation authority, and McCartney, 68, have been dating for about four years.
The pair posed for photos at a gala event at the Metropolitan Museum of Art on Monday.
McCartney was married for 29 years to American photographer Linda Eastman until her death of cancer in 1998. He then married British former model Heather Mills in 2002 but the union ended in a messy and high-profile divorce in 2008.
(Reporting by Jill Serjeant; editing by Dan Whitcomb)
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