House Oversight Committee Chairman Trey Gowdy said Wednesday that he will leave Congress after this year, the latest House Republican to resign or announce he won’t stand for re-election.

Mr. Gowdy (R., S.C.) is the second Oversight Committee chairman to quit in the past seven months. The post, one of the most powerful in Congress, allows for investigations into any aspect of the federal government. Mr. Gowdy became chairman in June when his predecessor, Rep. Jason Chaffetz of Utah, quit Congress to pursue a career as a television...