Time Warner Cable Inc., the No. 2 U.S. cable operator, immediately said it would drop the channel.
The sale's purchase price was undisclosed, but people with knowledge of the deal told The New York Times it was around $500 million, meaning Gore would receive about $100 million for his 20 percent Current ownership.
Al-Jazeera, owned by a Qatar government media subsidiary, said it plans to shut down Current, based in San Francisco, and start an English-language news channel in New York called al-Jazeera America.
The channel, which the Times said would likely be available in more than 40 million homes, would start later this year, with newscasts emanating from both New York and Doha, Qatar, al-Jazeera said.
Roughly 60 percent of the programming would be produced in the United States, with the balance coming from al-Jazeera's Doha-based English-language international news channel, al-Jazeera English.
Al-Jazeera -- which already has bureaus in New York, Washington, Los Angeles, Miami and Chicago -- intends to open several more in other U.S. cities and double its U.S. staff to more than 300 employees.
Current co-founder lawyer-businessman Joel Hyatt said in a letter to Current employees -- including some who are expected to lose their jobs -- that he, Gore and the other Current owners agreed to sell to al-Jazeera in part because "al-Jazeera was founded with the same goals we had for Current," including "to give voice to those whose voices are not typically heard" and "to speak truth to power."
He said he and Gore would join the al-Jazeera America advisory board.
Al-Jazeera said in a statement it wanted to start the U.S. news channel because almost 40 percent of al-Jazeera English's global online viewing comes from the United States.
"U.S. viewers have clearly demonstrated that they like the way al-Jazeera provides ... news," Director General Ahmed bin Jassim al-Thani said.
Al-Jazeera first went on the air Nov. 1, 1996, as an Arabic news and current affairs satellite TV channel and has since expanded into a 24-hour news network with several outlets, including Web and specialty TV channels in multiple languages.
It also plans to start Turkish-language al-Jazeera Turk this year, it said.
Since then, al-Jazeera English, which started in 2006, has gained recognition for its international coverage, although U.S. cable and satellite distributors have largely refused to carry the channel, the Times said, so it is available on television only in several U.S. cities.
The Times said al-Jazeera executives convinced Gore, Hyatt and the other Current owners it had the journalistic strength and financial backing to compete head-to-head with CNN and other U.S. news channels.
Current was started Aug. 1, 2005, after Gore and Hyatt bought small U.S. cable news channel Newsworld International from France's Vivendi Universal, now Vivendi SA.
The channel remained fairly obscure, showing viewer-submitted videos and documentaries, but broke through somewhat in 2011 when it shifted its format and hired Keith Olbermann, who brought his popular MSNBC program "Countdown" to the network.
Olbermann went on the air June 20, 2011, and was fired March 30, 2012, replaced by former New York Gov. Eliot Spitzer.
Current made ratings headway but on a typical night last year still only attracted an average viewership of 42,000 households, Nielsen Media Research said.
By contrast, Time Warner Inc.'s CNN has averaged about 700,000 households during prime time since late September, and Fox News Channel drew about 1.9 million, Nielsen said.
Time Warner Cable, the largest cable provider in New York and Los Angeles, took advantage of a change-in-ownership clause and said in a statement Wednesday night it would remove the service "as quickly as possible."
"Our agreement with Current has been terminated and we will no longer be carrying the service," the cable provider said.
It earlier warned it might drop Current because of its low ratings.