The Beatles legend, who is embroiled in a bitter divorce battle with Heather, offered the former model the payment to "tide her over" until the settlement is finalized.
A source told Britain's The Sun newspaper: "The £2 million (approximately $3.8 million) is all down to the fact Paul is a superbly warm and generous human being."
"He recognizes that there were good times. But the cash he agreed to hand over doesn't prejudice what the eventual settlement will be. It's to tide her over."
The former couple's lawyers are said to be locked in negotiations to determine Paul's exact wealth, following Heather's demands for $19,000 a day in her divorce settlement.
The 39-year-old reportedly needs $6.7 million a year just "to get by," but is willing to accept a one-off settlement of $77 million for a "high-speed" divorce.
Paul, 64, claims he is worth considerably less than the $1.59 billion fortune he is alleged to have and is refusing to meet Heather's demands.
A source added: "It all depends on exactly how much Sir Paul is worth and what contribution she can argue she brought to the marriage."
