Mr Boehner has been under pressure from the conservative wing of his party, and in particular over government funding for Planned Parenthood.
Aides say the speaker had planned to resign last year.
The announcement comes one day after the speaker hosted Pope Francis for a major address to the US Congress.
The BBC’s Anthony Zurcher says Mr Boehner has been walking a knife’s edge for years, trying to balance the business of Congress with a grass-roots conservative faction in his caucus that demanded confrontation and saw compromise as weakness.
Mr Boehner is expected to make a public announcement at 10:00 local time (15:00 BST).
Rep Bill Huizenga said in a tweet that the speaker made the announcement to his conference this morning.
In a statement, Mr Boehner’s staff said that he had intended to resign at the end of last year, but the surprise defeat of then House Majority Leader Eric Cantor “changed that calculation”.
The speaker’s resignation comes as Republicans have been deliberating over plans to defund women’s healthcare provider Planned Parenthood.
The organisation has come under fire from anti-abortion activists who claimed its employees were selling foetal organs.