The aircraft, piloted by Squadron Leader Hugh Nichols, was accompanied by two other F-35Bs from the United States Marine Corps.
They touched down at RAF Fairford in Gloucestershire just before 20:00 BST on Wednesday, watched by aviation enthusiasts waiting outside the base.
The supersonic jets were supported by refuelling tankers for the crossing.
They will be displayed at the Royal International Air Tattoo and the Farnborough Air Show over the next few weeks.
It is the first time an RAF F-35 has made the transatlantic crossing to the UK from the US.
Plans for the F-35 to display in Europe last summer were scrapped due to a technical problem.
The Lightning II, which is capable of short take off and vertical landing, will enter service with the RAF and the Royal Navy in 2018.
The UK will have 24 of the aircraft available on its two new aircraft carriers by 2023.
Its design uses stealth technology techniques to minimise its presence on radar, giving it "very low observable characteristics", according to the RAF.
Defence Secretary Michael Fallon said: "The F-35Bs are the most advanced fast jets in the world.
"Whether operating from land or from one of our two new aircraft carriers, they will ensure we have a formidable fighting force.
"They are part of our plan for a stronger and better defence - more ships, more aircraft, more troops available at readiness, better equipment for special forces, more being spent on cyber - to deal with the increased threats to our country."
An RAF F-35B Lightning II stealth fighter has landed in the UK for the first time after crossing the Atlantic.