Jain joined in 1986 and now serves as Executive Vice President of National Indemnity Company with overall responsibility for leading Berkshire's reinsurance operations.
Buffett, 87, who was treated for prostate cancer some years ago, described himself in "remarkably good health" in the CNBC interview.
He described Mr Abel and Mr Jain as having "Berkshire in their blood". Buffett had refused to name them, but investors who follow Berkshire had long included Jain and Abel on their short lists.
Charlie Munger, 94, who has worked at Buffett's side for more than four decades, will stay vice chairman.
Mr Buffett said he still goes to the office on Saturdays, but succession planning has always been part of the discussions among Berkshire Hathaway board members. Jain will oversee all of Berkshire's insurance operations.
Buffett said he had no idea about how or when things would go bad for Bitcoin and other cryptocurrencies, however: "When it happens or how or anything else, I don't know". He said jokingly, "I wasn't much to start with". He joined the company in 1992.More news: I won't forget what you said - Conte tells Mourinho
But on the stock market today, Berkshire's "B" shares traded 0.1% lower on the news, near 203. His Iowa-based unit now runs several power companies in the United States, Canada and Britain, as well as natural gas pipelines and solar and wind farms.
Mr Jain, 66, Berkshire's top insurance executive, will be vice chairman for insurance operations.
Buffett said he would not take a short position on bitcoin futures.
"If Jain become CEO it would be great, but the complexity of the insurance business requires someone there with more day-to-day supervision", Wedgewood's Rolfe said.
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.