The vehicle he was travelling in was hit by an improvised explosive device at around 02:00 local time (22:00 BST on Wednesday). After receiving surgery at Basra Air Station's field hospital he was airlifted back to the UK.
Pte Thompson was expected to make a full recovery from his injuries but his condition rapidly deteriorated soon after arriving back in the UK.
His family were with him when he died. They include his parents, two sisters, a brother who has joined the armed forces in his footsteps and fiancée Lucy.
"He loved the Army but loved his family more and constantly talked of being with them," the MoD said in a statement.
His commanding officer in Iraq, Lieutenant Colonel David Golding, said: "We are deeply proud of Kevin Thompson. He was an outstanding soldier, colleague and friend. Our sincere sympathy, thoughts and prayers are with his family and friends at this shattering time in their lives."
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