Republican fundraiser Elliott Broidy on Friday resigned from his post as deputy national finance chairman at the Republican National Committee, a person familiar with the matter said, following a Wall Street Journal report that he agreed to pay $1.6 million to a former Playboy model who said Mr. Broidy had impregnated her.

The deal was negotiated in late 2017 by Michael Cohen, President Donald Trump’s longtime lawyer who also serves on the RNC’s finance committee, the Journal reported. Mr. Cohen remains in his post, according...