The Canadian singer told BBC Radio 4's Desert Island Discs that the executive told him his music would not sell.
He told Buble he would only produce his music for $100,000 (Â£82,000) a track, just to get rid of him.
The singer has now sold more than 50 million albums around the world.
Buble started out as a swing crooner and also sings jazz and pop songs.
He told presenter Kirsty Young that David Foster, who has worked with Whitney Houston and Celine Dion, had told him: "You will never be signed to my label, I will never produce you.
"You are talented but I see no record sales for this genre of music.
"To dismiss me, [Foster] said, 'For $100,000 a track, I will produce on spec a record for you, and because I'm an executive of Warner Bros they'll get first right of refusal.
"And then he pushed me out the door thinking he would never see me again."
But the singer said the encounter made him determined to raise the money to work with Foster.
"What he didn't know was that I would go back to Vancouver and go bank to bank with a manager I had at the time and find an investor," Buble said.
"I flew back to Los Angeles and went to David's house, and he said 'What do you want?' And I said 'Mr Foster I have the money.'
"He couldn't believe I had come back. But he said, 'All right', and we started making the record."
Later, Buble explained, he asked Foster if he could speak to the president of Warner Bros and "plead" for the album to be released.
"I walked into the Warner Bros records' home in Burbank, and I don't think I'd ever been as terrified," Buble said.
"This executive named Tom Whalley came in the room and he said 'Why should we sign you? We have [Frank] Sinatra'."
"And I said 'With all due respect, Sinatra's dead, don't bury the music with him.' I said 'I'll work hard and help fill the void and we will keep this music alive together'.
"Three days later, I was on the treadmill and my grandfather was with me, and the doors flung open and my grandfather said 'Sunshine, you're with Warner Bros'."
Buble's eight song choices on Desert Island Discs include This Love of Mine by Sinatra, Lose Yourself by Eminem and My Love by Paul McCartney and Wings.
The singer said he would take The Power of Now by Eckhart Tolle with him to the island as his chosen book.
He said his luxury item would be a Rolex watch - he is an ambassador for the brand - "because I could at least figure out what time it was and how many days I had been there".
Desert Island Discs, featuring Michael Buble, was broadcast on BBC Radio 4 at 11:15 GMT on Sunday, 30 October and is now available online.
Update 3 November 2016: This story has been amended to make clear that Michael Buble is an ambassador for Rolex, information not provided in the original broadcast.
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Michael Buble has revealed how he went from bank to bank to raise hundreds of thousands of dollars to persuade a music executive to sign him at the start of his career.