South African teacher Pierre Korkie was also killed, just a day before he was to be freed after more than a year in captivity, said the charity that had negotiated his release.
Al-Qaeda in the Arabian Peninsula threatened in a video on Thursday to execute Somers, 33, kidnapped 15 months ago in Sanaa. It gave Washington three days to meet unspecified demands.
A senior US defence official said there were "good indications" al-Qaeda had moved the deadline up and "were preparing to kill him, on what would have been Saturday morning our time, which is why we moved as fast as we could".
"It was either act now and take the risk, or let that deadline pass. And no one was willing to do that."
South African teacher Pierre Korkie (AAP)
Commandos were dropped by helicopter in the dead of night 10km from where the hostages were being held in the southeastern province of Shabwa, the official said.
They made their way to the al-Qaeda hideout by foot, but were discovered about 100 metres away.
"When the element of surprise was lost, and a firefight ensued, we believe that is when (the hostages) were shot."
One of them - it is not clear who - died en route to a naval ship, the USS Makin Island, and the other on the operating table aboard the vessel.
Yemen said 10 militants were killed in the fighting and four of its own men wounded.
In May 2013, al-Qaeda seized Korkie and his wife Yolande, who was released in January. The couple had worked as teachers in Yemen for four years.
The Gift of Givers charity said logistical arrangements had already been put in place to fly Korkie, 57, out of Yemen Sunday.
"The psychological and emotional devastation to Yolande and her family will be compounded by the knowledge that Pierre was to be released by al-Qaeda tomorrow," it said.
"It is even more tragic that the words we used in a conversation with Yolande at 5:59 this morning was 'the wait is almost over'."
Obama said that since Somers was abducted, Washington had been using "every tool at our disposal" to try to secure his release.
"Luke was a photojournalist who sought through his images to convey the lives of Yemenis to the outside world," Obama added.
"He came to Yemen in peace and was held against his will and threatened by a despicable terrorist organisation."
"The callous disregard for Luke's life is more proof of the depths of AQAP's depravity," Obama said.
British-born Somers had worked as a freelance photographer for the BBC and spent time at local newspapers, including the Yemen Times before he was snatched off Sanaa's streets.
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