Around three million copies of Prince's new album, Planet Earth, have been given away with the Mail On Sunday.
Prince is also giving away the album at his concerts
The promotion is believed to be worth about £250,000 to the musician, whose hits include Purple Rain, Raspberry Beret and Money Don't Matter 2Night.
But the giveaway has angered retailers, who called it "an insult" to high street record stores.
It also dealt a blow to Prince's record label, Sony BMG, which has shelved plans to release the album in the UK.
Planet Earth has had largely positive reviews, with The Times saying it was "too good to be so lightly sold".
The US pop star also plans to give away copies to fans attending one of his 21 concerts at London's O2 arena next month.
That means it will reach many more listeners than the artist's last album, 3121, which only sold 80,000 copies in the UK.
Prince has sold more than 80m records worldwide
"It's direct marketing and I don't have to be in the speculation business of the record industry which is going through a lot of tumultuous times right now," said the Minneapolis musician when asked why he was giving the CD away.
"Prince has done this because he makes most of his money these days as a performing artist," the Mail on Sunday's editor, Peter Wright, told BBC Five Live.
"He's got a fantastic series of concerts coming up at the O2 Dome and this is a way of telling people what he's doing."
Wright confirmed that the newspaper had paid Prince for the licence to produce the CD, and had paid to press and distribute it, but hoped to make money by selling extra copies of the paper and extra advertising.
Nonetheless, the deal has sent shockwaves through the record industry, with the Entertainment Retailers Association being particularly vocal about their dissatisfaction.
Paul Quirk, co-chairman of the organisation, said the decision "beggars belief".
"The Artist formerly known as Prince should know that with behaviour like this he will soon be the Artist Formerly Available in Record Stores," said Mr Quirk, referring to a period in the 1990s when Prince famously stopped using his name in favour of a symbol.
However, music chain HMV has decided to stock Sunday's Mail, even though chief executive Simon Fox previously called the giveaway "absolutely nuts".