Graham holds the assets that remained after the Washington Post Co. sold its namesake newspaper to Amazon chief Jeff Bezos for $250 million last August.
In the new deal, Graham would swap the station, some Berkshire shares it owns and some cash in exchange for roughly 1.6 million Graham shares now held by Berkshire.
At Tuesday's close of $709.16, the Graham shares had a market value of $1.13 billion.
In early afternoon trading Wednesday, the stock was up 3.3 percent to $732.50.
Berkshire reported holding 1.7 million shares as of the end of December, about 23.4 percent of the Graham shares outstanding.
The trade would leave Berkshire with just about 100,000 shares.
In a statement announcing the deal, Buffett said, "While this transaction will greatly reduce our position in Graham Holdings, our admiration for the company and its management is undiminished."
That admiration goes back decades. Buffett, a newspaper fan going back to his childhood when he delivered the Post, bought the stock for Berkshire for about $11 million in 1973.
As a company director, he developed a close friendship with then-CEO Katharine Graham, who was helping to steer the Post through the waves it created with its coverage of the Watergate scandal. She died in 2001
While Berkshire had already disclosed it was talking with Graham Holdings about a possible trade, the transfer of a major-market television station was something of a surprise.
Berkshire has owned stakes in companies with television stations and helped finance Capital Cities' purchase of ABC in 1985. It hasn't however, had a TV station as a subsidiary.
Berkshire has been buying newspapers in small and medium-sized towns, including Buffett's home town of Omaha , Neb., because he believes the local news and community information they deliver will allow them to overcome new competition from national Internet news sources.
He may be making a similar bet on WPLG's local news coverage, although it also faces competition from other stations in the city.
It's also possible there weren't that many options in the appropriate price range among Graham's assets, with include Kaplan, its educational services company, several other TV stations, Slate, and Foreign Policy magazine.
By doing a swap instead of simply selling the now highly appreciated shares, Berkshire should be able to avoid a massive tax bill.
As The Streetpoints out, Berkshire could be setting a pattern for the future by using exchanges to get out of big stock holdings. In December, it traded $1.4 billion worth of Phillips 66 stock for one of the company's subsidiaries.
-By CNBC's Alex Crippen. Follow him on Twitter @alexcrippen