Cantor was expected to announce his plans at a late-afternoon meeting of the party's rank and file, less than 24 hours after the Virginia Republican lost a primary election to David Brat, a little-known and underfunded rival backed by tea party groups.
Before the announcement, jockeying already had broken out among fellow Republicans eager to move up the House leadership ladder — or establish a foothold on it.
Rep. Kevin McCarthy of California, the party whip and third-ranking leader, informed fellow Republicans he intended to run to succeed Cantor, and Rep. Pete Sessions of Texas also made clear his interest.
Rep. Peter Roskam of Illinois, the chief deputy whip, and Rep. Steve Scalise of Louisiana quickly jumped into the expected race to succeed McCarthy.
Cantor's office declined to confirm his decision, which was reported by numerous Republican aides as well as lobbyists who said they had been informed of the plans. His intention was to declare his decision to step down from the leadership on July 31.
One Republican said he feared the effects of Cantor's defeat could be debilitating for the party and the government.
Interviewed on MSNBC, Rep. Peter King, R-N.Y., said he was worried that Cantor's stunning loss may lead to even more congressional gridlock. Asked if he thought immigration legislation was dead, he replied, "I'm concerned that Ted Cruz supporters, Rand Paul supporters, are going to use this as an excuse" to shut down the government.
"This is not conservatism to me," King said. "Shutting down the government is not being conservative."
The resignation would mark a swift end to a quick rise to power for Cantor, 51, who was elected to Congress in 2000, was appointed to the leadership two years later, and then rose steadily to become the second-most powerful Republican in the House. In that post, he was the most powerful Jewish Republican in Congress, and occasionally was seen as a potential rival to Speaker John Boehner but more often as a likely successor.
He was defeated Tuesday by primary rival David Brat, an economics professor making his first run for office in an underfunded campaign that benefited from the support of tea party groups.
Brat campaigned as a foe of immigration legislation, and said Cantor was likely to help immigrants living in the United States illegally gain amnesty if given a new term in the House.
Interviewed on MSNBC, Brat declined to spell out any policy specifics.
"I'm a Ph.D. in economics, and so you analyze every situation uniquely," he said.
Brat begins the fall campaign as a decided favorite in the race against Democratic rival Jack Trammell in a solidly Republican Richmond-area district.
His primary triumph was by far the biggest of the 2014 campaign season for tea party forces, although last week they forced veteran Mississippi Sen. Thad Cochran into a June 24 runoff and they hope state Sen. Chris McDaniel will achieve victory then.
Tuesday's outcome may well mark the end of Cantor's political career, although at his age he has plenty of time to attempt a comeback.
The impact of Cantor's surprise loss on the fate of immigration legislation in the current Congress seemed clear. Conservatives will now be emboldened in their opposition to legislation to create a path to citizenship for immigrants living in the country illegally, and party leaders who are sympathetic to such legislation will likely be less willing to try.
Cantor has compiled a solidly conservative voting record in his tenure, but he was sometimes viewed with suspicion by tea party activists who said he had been in Congress too long and was insufficiently committed to blocking immigration legislation. Many party officials argue that Republicans must temper their hard line on immigration if they are to compete effectively in future presidential elections.
Already on Wednesday, Hillary Rodham Clinton, a potential Democratic contender, said Cantor "was defeated by a candidate who basically ran against immigrants."
Democrats, underdogs in the struggle for control of the House this fall, sought to cast Cantor's defeat as evidence that the Republican Party and tea party groups were one.
"The Republican Party has been completely swallowed by the tea party. I mean, any debate over whether the tea party controls the Republican Party has ended," Rep. Debbie Wasserman Schultz of Florida, the Democratic national chair, said on MSNBC.