The former Beatle is understood to be planning to wed the 49-year-old American heiress, whom he has been dating for almost a year.
Ms Shevell - whose father heads the £250 million family haulage business - obtained her full divorce from Mr Blakeman last month.
The divorce was made final by the US Supreme Court of the State of New York on December 9, after she had been legally separated from him for one year and sixty days.
Friends said the split was "amicable".
Ms Shevell, who has a 17-year-old son with Mr Blakeman, has apparently been given the seal of approval by Sir Paul's children, including fashion designer Stella McCartney. She never hid her opposition to her father's union with Heather Mills.
A friend told the Sunday Mirror: "Getting Stella's seal of approval was very important for Paul. All Paul's children had massive reservations about Heather - but it was Stella who was the most vociferous."
The influential East Coast family of Sir Paul's first wife Linda - the Eastmans - are also said to have given the new relationship their blessing.
Sir Paul and his first wife were friends with the Blakemans before Linda's death from cancer in 1998, as they knew each other from holidaying in the upmarket coastal resort of The Hamptons on Long Island.
Friends believe Ms Shevell is a much better fit for Sir Paul than Heather Mills, coming from a similar background to Linda.
A source said: "Nancy has been through a lot, not least overcoming breast cancer. She also comes from a similar wealthy East Coast background to Linda. They shared a similar outlook on life. She joined the family firm in the 1980s and has become wealthy in her own right. It makes everyone comfortable that she is clearly not after Paul's money."
However, Ms Shevell does differ in her politics. She is a meat-eating Republican, unlike the more liberal and staunchly vegetarian ex-Beatle.
Sir Paul, 66, has seemed happy to appear in public with Ms Shevell from the early days of their relationship.
Last March the pair were photographed together while on the small Caribbean island of Jumby Bay, near Antigua, little more than a week after his £24m divorce from Heather Mills was granted by the High Court