Mr. Trump did not specify how Mr. Burch, who is married to a Yemeni woman, was freed. It also was not clear who had abducted Mr. Burch, although former American officials said he was not being held by Al Qaeda.

Image Mr. Burch is an engineer at a Yemeni oil company and is married to a Yemeni woman. Credit... Nadia Forsa

Working closely with American forces, the United Arab Emirates has stationed ground troops in Yemen to fight Houthi rebels in the country’s ongoing civil war. American officials have previously told The New York Times that freeing Mr. Burch likely would have required a raid; a State Department spokesman on Monday said the United Arab Emirates was “crucial” to securing his release.

Two American officials discussed the details of the case on Monday on condition of anonymity.

Mr. Burch, who had been working for oil companies in Yemen for years, was 63 when he was forced from his car by unidentified gunmen in September 2017. At the time, Nadia Forsa, Mr. Burch’s wife, said in a phone interview that “they did it in broad daylight in front of everyone.”

Kidnappings of Americans and other Westerners are common in Yemen, a poor country that has been devastated by years of civil unrest. Houthi rebels and affiliates of Al Qaeda often attempt to ransom hostages for money or accuse them of being spies.

At the time of Mr. Burch’s abduction, no group claimed responsibility.

Mr. Burch began working on oil rigs in Yemen in the mid-1990s. He traveled between the United States and Yemen before moving there permanently, according to Stephen Burch, his son from his first marriage, in an interview shortly after he was taken in 2017.