The Beatles legend reportedly settled out of court because he is desperate to keep details of the split private.
A source told Britain's News of the World newspaper: "This way Paul gets to have the divorce in private, which is all he ever wanted and Heather avoids risking her case falling apart."
Heather, 39, who reportedly demanded a $197 million settlement, was said to be "delighted" with the deal, which entitles her to the couple's $7.9 million mansion in St John's, London, and Paul's $11.8 million Beverly Hills property.
Paul's daughters Stella and Mary are allegedly furious because they wanted to see Heather - who claimed Paul, 64, was verbally and physically violent during their four-year marriage - discredited in court.
The source added: "Stella and Mary are baying for blood. Their poor dad has been dragged through the mire by this woman and they all wanted to see his name cleared on the record, in public."
A spokesman for Paul has declined to comment. Meanwhile, Paul and Heather will go to court next month to resolve their security row.
Heather insists she is entitled to a professional bodyguard after receiving death threats, but Paul is refusing to pay for one.
