Captain Thomas Clarke, Warrant Officer Spencer Faulkner, Corporal James Walters, all of the Army Air Corps (AAC) lost their lives together with Flight Lieutenant Rakesh Chauhan of the Royal Air Force and Lance Corporal Oliver Thomas of the Intelligence Corps.
Their aircraft went down in Kandahar province during a routine flight on Saturday morning.
The Ministry of Defence (MoD) has denied claims by the Taliban that insurgents shot the helicopter down, with initial investigations indicating a "tragic accident" rather than enemy action.
Group Captain Richard Maddison, Station Commander at RAF Odiham, said: "I am extremely saddened to hear of the loss of Captain Thomas Clarke, Flight Lieutenant Rakesh Chauhan, Warrant Officer Spencer Faulkner and Corporal James Walters, all who served at Royal Air Force Odiham.
"My deepest sympathies are with their families and friends at this most difficult time, and also with the family of Lance Corporal Oliver Thomas, who was not from Royal Air Force Odiham but who was also on the Lynx aircraft."
The Station Commander described the men based at RAF Odiham in north Hampshire as "professional and enthusiastic".
Captain Clarke, 30, from Cowbridge in Wales, was described as a "rising star."