Sgt Danny Nightingale said outside court after being released: "Thank you to the world for being so kind".
His wife Sally said she was "very, very happy" and that she had "fought for this and got justice today".
More top news
Johnny Depp's band the Hollywood Vampires are due to play in Stockholm, Sweden, but face calls for the gig to be boycotted.
The launch of a medium-range missile took place around 5.20am Seoul time, off the country's east coast, an official said.
The world-famous theoretical physicist described the US presidential candidate as a "demagogue" to Good Morning Britain.