Morgan Creek Capital's founder and chief investment officer, Mark Yusko, accepted Buffet's offer on Tuesday. His firm manages a fund of hedge funds and also does direct and private investments.

The "Oracle of Omaha" told CNBC's Becky Quick on Tuesday that he is willing to do another bet on active versus passive as long as anybody wants to put up "a significant percentage of their net worth" on the wager.

Warren Buffett already won once betting passive investing in a simple index fund can beat a basket of hedge funds over 10 years. Now a new challenger is stepping up.

"I accept," said Yusko, whose firm manages $1.8 billion, in a phone interview. "It's an important time in terms of the market cycle. I think it's important to be aware about the propensity of investors to chase hot returns at the peak of the cycle. It is a better time to get hedged."

The bull market in stocks turns 9 years old in March.

The investment manager said he is willing to accept the exact terms as Buffett's previous bet with hedge fund manager Ted Seides. Yusko said he has not talked or reached out to Buffett yet.

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A decade ago, the billionaire investor made a million-dollar bet with Seides, a former co-manager of ProtegePartners, that the S&P 500 will beat a basket of fund of hedge funds over the next 10 years, ending this year. The Berkshire Hathaway chairman and CEO will likely win that bet by a large margin.

Seides conceded he lost the bet earlier this year.

Buffett, who is 87, still won the original wager even after a vicious bear market occurred as a result of the housing crisis. The new bull market began in March 2009.

Hedge funds lost out to simple index funds as an economic recovery and extraordinary Federal Reserve stimulus lifted the majority of stocks and assets during this latest run.

This second bet, if Buffett accepts, would be under relatively smooth economic and market conditions. Some investors say they are too smooth and therefore ripe for a disruption where hedge funds could thrive. That's apparently Yusko's bet.

But investing legend Buffett said earlier Tuesday that wouldn't matter.

The S&P 500 "will absolutely kill every one of the fund of funds," Buffett said on CNBC's "Squawk Box" on Tuesday. "Passive investment in aggregate is going to beat active investment because of fees."