He is expected to step aside as majority leader on July 31. The decision sets up a leadership scramble among Republicans in the House, which is led by Speaker John Boehner of Ohio.
The heavily favored Cantor lost Tuesday to college professor and political novice Dave Brat, who triumphed in the Richmond-area district with tea party support.
Cantor is expected to address reporters later on Wednesday.
Most Republicans had viewed Cantor, 51, as the most conservative member in the House leadership and a likely successor to Boehner.
Republican sources said Boehner is more likely to stay on and help build a new leadership team without a clear successor.
Boehner on Wednesday called Cantor a “good friend” and a “good leader” for Republicans.
Conservative members are already demanding someone from a red state be elected to represent their views at the leadership table.
The election for Cantor’s GOP position is next Thursday, according to two Republican sources.
Rep. Pete Sessions of Texas told reporters he’s planning to run for Cantor’s post. Current House GOP Whip Kevin McCarthy of California also is expected to do so, but Rep. Cathy McMorris Rodgers of Washington State, the top women on the leadership team, will stay put.
GOP strategist John Feehery, formerly a top Republican congressional aide, said Cantor’s defeat throws the GOP conference into chaos and will make it harder to get anything done.
Although Cantor dramatically outspent Brat in Virginia’s 7th Congressional District race and most political observers anticipated he would win easily, the cash advantage didn’t alter the outcome and he lost convincingly.
Cantor fell by 10 percentage points although turnout was low.
“Eric Cantor lost this race as much as Dave Brat won it. He simply violated rule number one of politics: go home,” said CNN Chief National Correspondent John King. “This is Eric Cantor’s fault. He was in Washington on primary day. Not back in his district.”
Brat ran an anti-establishment campaign, hitting Cantor for his ties to Washington and characterizing him as out-of-touch with Virginians.
He also slammed Cantor’s support for proposals allowing children of those who enter the country illegally the ability to obtain some type of legal status, chalking the stance up to amnesty and insisting Cantor’s views would hurt the economy.
Brat, who predicted a shocker on Tuesday, is an economics professor at Randolph-Macon College. His Democratic opponent in November, Jack Trammell, also teaches at the school outside Richmond. Trammell was nominated at a party convention and is thought to have a very tough road ahead.