 Major Alexis Roberts was killed in Afghanistan |
The soldier, serving with the 1st Battalion The Royal Gurkha Rifles, was returning to Kandahar Airfield on Thursday when the blast happened.
Maj Roberts, 32, lived in Kent with his wife and two daughters.
Prince William said he was "deeply saddened" at the death of Maj Roberts, his platoon commander at Sandhurst, whom he described as "a good friend".
"At this time, his thoughts and prayers are with Lex's wife, Susie, their two young daughters, Alice and Freya, and with all his family and friends," a statement issued by Clarence House added.
The death has taken the number of British troops killed in Afghanistan since the start of operations in 2001 to 82.
It is the first death in the conflict of a soldier serving with the Gurkhas.
Defence Secretary Des Browne said: "I was greatly saddened by the news of Major Roberts' tragic death.
"He was an extremely experienced officer and who was, quite obviously, held in high regard by his superiors, peers and those who worked for him.
"My heart goes out to his family and friends as they come to terms with their loss."
 |  The British Army has lost one of its finest prospects and the nation has lost a dedicated servant  Lt Col Jonny Bourne MBE |
Maj Roberts was usually an Officer of 2nd Battalion The Royal Gurkha Rifles, although he had been serving in Afghanistan with The 1st Battalion when he was killed.
Maj Roberts, and two soldiers who were injured, were taking part in an operation in nearby Helmand Province when they were hit.
Lieutenant Colonel Jonny Bourne MBE, Commanding Officer 1st Battalion The Royal Gurkha Rifles, paid tribute to the soldier.
He said: "In Major Lex Roberts, both battalions of the Royal Gurkha Rifles have lost a dear friend and a treasured officer.
"The British Army has lost one of its finest prospects and the nation has lost a dedicated servant, a demonstrably warm-hearted man of profound integrity and courage - quite simply, a very special human being."
