WASHINGTON—Special counsel Robert Mueller presented his long-awaited report to the Justice Department on Friday, ending his nearly two-year investigation that has loomed over the Trump presidency and likely setting up a political battle over what he has found.

In a letter to the majority and minority leaders of the House and Senate Judiciary Committees, Attorney General William Barr said Mr. Mueller had concluded his investigation of Russian interference in the 2016 election and related matters, and he said he would be able...