The Houthis first took control of Sanaa in September, and Hadi has been held as a virtual prisoner at his residence since then.
As Reuters notes, Hadi, a former general, became increasingly frustrated with his situation and "blamed the Houthis' control of the capital Sanaa for impeding his attempt to steer Yemen toward stability after years of secessionist and tribal unrest, deepening poverty and U.S. drone strikes on Islamist militants."
Yemen's parliament is expected to hold an emergency meeting on Sunday to discuss the resignations, The Associated Press says.
(For a guide to the situation, see a story from NPR's Greg Myre here. And, if you're looking for a primer on the Houthis, Greg has a post here.)
The New York Times describes Hadi as "a weak statesman who has been a staunch ally in Washington's battle against Al Qaeda and other Sunni extremists, may have decided to cede control, feeling he was outgunned by the Houthis, the Shiite rebels who took up arms against the government after years of political grievances. Or he might have announced he was stepping down, expecting that the Houthis would be willing to strike a deal because they may not be interested in governing one of the world's most impoverished and combustible nations."
And the Post notes:
"The crisis threatens to weaken Washington's campaign against al-Qaeda in the Arabian Peninsula (AQAP), which is based in Yemen and has actively targeted the United States and Europe. The government's collapse could also plunge Yemen into full-scale civil war. The Houthi rebels are widely considered to be backed by Shiite-majority Iran, although they deny it. Yemen's population is majority Sunni, and there is a strong separatist movement in the Sunni-dominated south."
"The resignations in Yemen are likely to set off alarms not just in Washington but in Sunni Arab capitals, especially in neighboring Saudi Arabia, which has backed Hadi's government with billions of dollars and views Iran as its foremost regional rival."
Outgoing Secretary of Defense Chuck Hagel, in an interview that will air Monday on NPR's Morning Edition, says Washington is still working through the sudden change in government in Yemen.
"We still have resources there. We still want to participate and cooperate and partner with" the Yemenis, Hagel tells ME host Steve Inskeep.
"We have to wait until the Yemenis have decided who is going to run their government," Hagel said, adding that "the phones are still answered at the various ministries in Sanaa.
That uncertainty in Yemen is no doubt exacerbated by the announcement early today that Saudi King Abdullah has died. Abdullah effectively ruled the kingdom for two decades after his predecessor, King Fahd, suffered a stroke in 1995.
Daniel Benjamin, a former U.S. State Department counterterrorism chief who is currently director of Darmouth College's Dickey Center for International Understanding, says "it's a safe bet that things are not likely to get better" in Yemen.
"We now have a bizarre situation in which the Houthis, who are the enemy of our enemy AQAP, are really not our friends and will likely inhibit our efforts to build the capacity of the Yemeni military and security forces," he says. "While more AQAP energy will go into fighting the Houthis than before, the net effect is that there will be more chaos."