The show - created by Shawn Ryan (The Shield) and Karl Gajdusek - debuted on ABC in the US last month, attracting over 9m viewers.
Last Resort will receive its UK premiere on Tuesday, October 30 at 8pm, Sky1 has now confirmed.
Andre Braugher and Scott Speedman star in the series, which follows the crew of a nuclear submarine who refuse to fire their missiles on Pakistan.
The actions of Navy captain Marcus Chaplin (Braugher) soon reveal a vast government conspiracy, with the crew of his craft - the USS Colorado - being marked for death.
"Last Resort is a tense, edge of your seat thriller and I'm confident that it will resonate with our customers," said Sky1's Acquisitions Manager Lucy Criddle. "It's great to be continuing our partnership with Sony Pictures Television on another exemplary piece of television drama."
Other recent US acquisitions from UK broadcasters include ABC's Scandal and Nashville - both of which will air on More4 - and The CW's Beauty and the Beast, picked up by UKTV channel Watch.
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Watch a trailer for Last Resort below: