Jack Bristow, 23, of Hobbyhorse Lane, Sutton Courtenay, Oxfordshire, was a passenger in a white Mercedes-Benz Sprinter when a falling tree landed on it.
Emergency services attended the incident, which occurred in Old Odiham Road in Alton at around 11.45am on Friday, February 18, but Mr Bristow was pronounced dead at the scene.
The driver the van, Callum Smith, was seriously injured and taken to Southampton General Hospital, where he remains in a stable condition.
Paying tribute to Mr Bristow, his family said: “We write this with broken hearts. The loss of a son is something you could ever be prepared for.
“Jack was a much loved son, grandson, boyfriend and father.
“Everyone knew Jack and everyone loved Jack, how could you not! He was a joker, loved to have a laugh and a good time.
“He lived life to the full, and had done and been through so much in his young 23 years.
“We are absolutely devastated and there are not enough words to describe our pain.
“But he lives on through his son Harvey. Rest in Peace Jack, we love you more than you will ever know.”
Officers continue to investigate the exact circumstances of the collision.
A police spokesman said: “If you have any information which may assist our enquiries, but have not yet spoken with officers, then please call 101, quoting the reference 44220068638.”