WASHINGTON—Secretary of State Mike Pompeo has announced that he will designate Yemen’s Iran-backed Houthi rebels as a “foreign terrorist organization” as time runs down on the Trump administration. The designation will take effect on Jan. 19, one day before president-elect Joe Biden is set to take office. The announcement Sunday comes as Pompeo and his top aides rush to complete actions they believe will cement their legacy and the president’s. In addition to the Houthi designation, Pompeo in coming days is also expected to likely re-designate Cuba as a “state sponsor of terrorism,” according to several administration officials. Both moves will impose or re-impose sanctions on the targets and may complicate the incoming Biden administration’s diplomatic plans. On Saturday Pompeo angered China when he declared restrictions on U.S. diplomatic contacts with Taiwanese officials to be null and void. In addition, Pompeo plans before leaving office on Jan. 20 to draw …