Abel and Ajit Jain are being added as directors.
"Today's news codifies the importance of Greg Abel and Ajit Jain to not just their current businesses, but their future authority once Buffett relinquishes the CEO title", he added. Buffett had refused to name them, but investors who follow Berkshire had long included Jain and Abel on their short lists.
In connection with their election to the Board of Directors, Buffett, Berkshire Hathaway's Chairman and CEO, appointed Abel to be Berkshire Hathaway's Vice Chairman - Non-Insurance Business Operations and Jain to be its Vice Chairman - Insurance Operations.
The hard-driving Buffett, who has been reluctant to name a successor, said in the past that Berkshire's board knows who would take over if something were to happen to him.More news: The Overwatch League will be broadcast on Twitch
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Mr Abel, 55, now chief executive of Berkshire Hathaway Energy, has been named as vice chairman for non-insurance business operations.
Buffett, 87, who was treated for prostate cancer some years ago, described himself in "remarkably good health" in the CNBC interview.
"I love what I do at Berkshire", he said. He joined the company in 1992.
In late-morning trading, Berkshire Class A shares rose $2,010 to $306,530 and its B shares rose $1.61 to $204.63. "Why in the world should I take a long or short position on something I don't know anything about?" Speculation had centered on Abel and Jain as possibilities.
Its investments include Geico, the Kraft Heinz Co, Fruit of the Loom and Acme Brick Company, as well as Northern Powergrid subsidiaries, which serve about 3.9 million customers in the UK.