Forces loyal to exiled President Abd-Rabbu Mansour Hadi also took Aden's central district of Khormaksar on Tuesday, and aid sources reported fighting around the port area.
Assisted air support from an Arab coalition, Yemeni forces launched a wide-ranging assault in Aden this week to reclaim territory held by the Iranian-allied Houthis.
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"Aden International Airport and Khormaksar have been cleared of Houthi and Saleh elements by armed forces backing Yemen's legitimacy and the popular resistance forces, in coordination with and with direct support by the coalition," Yemeni government spokesman Rajeh Badi said.
He said he expected Aden to be cleared completely within the coming days.