Cantor told the newspaper he has asked Gov. Terry McAuliffe to call a special election for his district that coincides with the Nov. 4 general election. That would enable his successor to take office immediately.
Cantor's announcement came hours after he stepped down as House majority leader Thursday. Cantor had previously said he would serve his full term, which would have ended in January.
Cantor lost to Dave Brat, an underfunded, tea party-backed opponent, in his Republican primary in June.
"I want to thank Eric for his service to the Seventh District and to the entire Commonwealth," Brat said in a statement. "The time one has to sacrifice to be an elected official is enormous, and he has sacrificed a great deal to serve the people. I also want to thank him for his endorsement. I wish Eric and his family the best in their future endeavors."
Cantor, 51, is a seven-term House veteran who before his defeat had been seen as a potential rival â?? and likely successor â?? to House Speaker John Boehner, R-Ohio. Though he had a conservative voting record, he was distrusted by some tea party supporters who suspected he might be too eager to reach compromise on immigration legislation.