Sir Paul and Ms Shevell have been together for four years and got engaged in May The wedding is expected to take place at Old Marylebone Town Hall, which is where Sir Paul married first wife Linda Eastman - also an American - in 1969.
She died in 1998 and Sir Paul, 69, split from second wife Heather Mills during an acrimonious divorce in 2008.
Mirror showbiz journalist Clemmie Moodie said she expected Sunday's wedding to be a low-key affair.
"Given his last marriage to Heather Mills obviously was a fairly lavish, spectacular do and look how that ended... I think this time round it's going to be a far quieter, more civilised affair," she said.
"It's just close family, a few friends - we believe about 30 people - so far more intimate."
Paul McCartney married Linda Eastman in 1969 Ms Shevell, who was married for 20 years to American lawyer and political candidate Bruce Blakeman, became engaged to Sir Paul in May.
The couple began dating four years ago in the upmarket Hamptons area of Long Island.
Life-long Beatles fan Chiara Amato said she had sat outside the register office every day since September 29 in anticipation of the couple's wedding.
She said: "This marriage is going to last. She seems to be really nice and deeply in love with him. I have been listening to The Beatles since I was six-years-old. I have been to see Sir Paul in concert 27 times."
Sir Paul's eldest daughter, Mary, also married at the register office last year.
Ms Shevell is a board member of New York's transportation authority and vice-president of her family haulage firm.
But the wedding is expected to mean an end to her work in the family business and her leaving her position on the board of the transportation body.
Ms Shevell told the New York Post she would "love" the couple to live in the US but she would "probably" move to England after the wedding.