"The airport was completely cleared and is under control," coalition commander for the Red Sea coast, Abdul Salaam al-Shehi, said in a video posted by the United Arab Emirates' official WAM news agency.
Residents said clashes at the airport have abated but coalition warplanes were bombing positions held by the Houthis as the group dug in to defend Hodeida, its sole port and the lifeline for millions of Yemenis.
The Saudi-led coalition launched the campaign to retake the strategic Red Sea city and port of Hodeida last Wednesday, with Emirati troops leading forces loyal to the former Yemeni government. Saudi Arabia has provided air support, with targeting guidance and refueling from the US.
The airport lies just eight kilometers (five miles) from the city's port, through which three-quarters of Yemen's imports pass, providing a lifeline for some 22 million people dependent on aid. The port city has been under Houthi control since 2014.
The offensive has faced criticism from international aid groups, who fear a protracted fight could force a shutdown of the port and potentially tip millions into starvation. Some 70 percent of Yemen’s food enters via the port, as well as the bulk of humanitarian aid and fuel supplies. Around two-thirds of the country’s population of 27 million relies on aid and 8.4 million are at risk of starving.
UN envoy Martin Griffiths held four days of talks in the capital Sana’a in a bid to avert an all-out battle for the city but flew out on Tuesday without announcing any breakthrough.
The Houthis seized control of Sanaa in September 2014, later pushing south toward the port city of Aden. The Saudi-led coalition attacked Yemen in March 2015 and has faced criticism for a campaign of airstrikes that has killed civilians and destroyed hospitals and markets.
Reuters, AP and AFP contributed to this story.