Dempsey tells The Associated Press his resignation will take effect Aug. 7.
The Republican from St. Charles first was elected to the House in 2000 and has served in the Senate since 2007.
He is the fifth Missouri lawmaker to resign in the past year. But Dempsey says his departure is unrelated to recent scandals involving colleagues. Last week, Democratic Sen. Paul LeVota said he would resign while denying allegations he sexually harassed interns. In May, Republican House Speaker John Diehl resigned after exchanging sexually suggestive text messages with an intern.
Dempsey said he hopes to announce his new private-sector job soon.