The Beatles legend - who split from Heather in May 2006 following a four-year marriage - has agreed to give the former model a lump sum of $30 million in what could be the largest divorce deal in British legal history.
A source said: "We're extremely close to a resolution. The figures have been agreed."
Heather, 39, will reportedly receive a further $7 million every year until their three-year-old daughter Beatrice turns 18.
Paul, 65, will reportedly pay all the expenses for Beatrice's schooling, travel, security and nannies and the pair will share custody of their daughter.
The divorce deal is also said to include a clause banning the pair from speaking publicly about the breakdown of their marriage.
The source told Britain's Daily Mail newspaper: "Negotiations have been drawn out because Heather wants her story told. Paul's lawyers are saying she can't talk about the marriage. But Heather's argument is that that's a very gray area, like if she wants to update her biography for example. It's a very complex agreement."
Heather, who recently bought a $821,000 house in Slovenia, allegedly won't receive any property in the deal.
Representatives for Paul and Heather said they would not comment on any progress with divorce proceedings.
