Mr Buffett built Berkshire Hathaway from a failing textile maker into a $628bn (£452bn) investment juggernaut.
Although he is 90 years old, Mr Buffett has given no indication he plans to step down.
However, there has been speculation for more than a decade about who will succeed him.
“The directors are in agreement that if something were to happen to me tonight, it would be Greg who’d take over tomorrow morning,” Mr Buffett confirmed to CNBC.
Mr Abel helped build Berkshire Hathaway’s energy unit into a major US power provider.
Since 2018, the Canadian has been a vice-chairman, overseeing Berkshire Hathaway’s non-insurance businesses.
Vice-chairman Charlie Munger may have tipped the company’s hand by accident at Berkshire Hathaway’s annual meeting over the weekend.
When answering questions about the company’s decentralised business model, Mr Munger emphasised its importance and said, “Greg will keep the culture.”
Mr Munger made no mention of Ajit Jain, another well-regarded contender for the job who had overseen Berkshire’s insurance businesses.
Mr Jain’s age appears to have played a role in the decision.
At 58 years old, Mr Abel is a decade younger than Mr Jain, and Mr Buffett told CNBC that Abel’s relative youth was significant.
“The likelihood of someone having a 20-year runway though makes a real difference,” he said.
Mr Buffett is arguably the world’s most successful investor.
Berkshire Hathaway owns more than 60 companies, including insurer Geico, battery-maker Duracell and restaurant chain Dairy Queen.
It also has major stakes in Apple, Coca Cola, Bank of America and American Express, among others.
In March, Mr Buffett joined the exclusive $100bn (£72bn) club after Berkshire Hathaway shares hit record levels.
Microsoft founder Bill Gates, Amazon founder Jeff Bezos and Tesla’s chief executive Elon Musk have also passed the milestone.