The Type 45 destroyer left Portsmouth last month to protect Britain's air bases in Cyprus.
Kataib Hezbollah says the release comes on condition that she leave Iraq immediately.
Trump has backed himself into a corner with threats that the US military can't feasibly carry out in a one fell swoop, military experts told the BBC.
Trump warns "a whole civilisation will die tonight" unless Iran reaches a deal.
Attacks have targeted bridges, steel plants and pharmaceutical facilities, verified videos show.