But Congress dropped the legislation after thousands of websites staged a massive protest, claiming the bills would stifle innovation and restrict free speech.
The new Interagency Trade Enforcement Center will bring together a wide range of trade experts, including analysts and lawyers who will examine enforcement issues, the White House said.
Obama first announced the agency in his State of the Union address last month and touted the office in a speech Tuesday.
U.S. Trade Representative Ron Kirk will pick the center's director, and Commerce Secretary John Bryson will choose a deputy deputy director, according to a statement.
The agency will work with the White House's Intellectual Property Enforcement Coordinator to combat copyright infringement.
The office will also address currency manipulation and other issues.