"US Special Operations Forces conducted a mission in Yemen to rescue a US citizen, Luke Somers, and any other foreign nationals held hostage with him by Al-Qa'ida in the Arabian Peninsula (AQAP) terrorists," Hagel said in a statement released during a visit to Kabul.
"Both Mr Somers and a second non-US citizen hostage were murdered by the AQAP terrorists during the course of the operation."
Hagel added that yesterday's operation was undertaken when "there were compelling reasons to believe Mr Somers' life was in imminent danger."
"The rescue attempt took place in central Yemen and was conducted in partnership with the Government of Yemen.
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"Yesterday's mission is a reminder of America's unrelenting commitment to the safety of our fellow citizens -- wherever they might be around the world.
"I commend the troops who undertook this dangerous mission."
A charity that had been involved in negotiations said the second dead hostage was Pierre Korkie from South Africa.