The chopper was an RAF-operated Puma, which can transport around 20 soldiers.
It flew over the city centre and Leeds Bradford Airport, although it did not land.
Pumas are manufactured by the French firm Aerospatiale, and are also used by the SAS and several foreign armies.
The model has seen service in the Gulf War, Falklands War and recent conflicts in Iraq.
The RAF took delivery of its first Pumas in 1971, part of an original order of 48. One operated by the Argentine navy was captured during the Falklands and shipped back to the UK, where it was used for training purposes.
They are also sent to disaster zones during relief and peacekeeping operations, and can evacuate casualties.
In 2007, a Puma crashed near Catterick Garrison in North Yorkshire, killing an RAF pilot and two soldiers. An inquest found the crew were not skilled in performing low-flying manoeuvres and that one man had shouted out a phrase from the film Top Gun during the flight.
Civilian operators use Pumas to transport North Sea oil workers to offshore platforms.
All photos by Andrew Easby.