Luke Gething, 20, of Somerset Fields, Bentley, and 22-year-old Thomas Matthew Price, of Baverstocks, Alton, were both killed following the single vehicle accident near Winchester last week.
The accident happened at 6.30am on the B3404 Alresford Road, one mile east of St Swithun’s School.
The Blue Ford Fiesta had been travelling in the direction of Winchester when it left the carriageway and collided with a tree.
Mr Price’s family said: ‘Tom was sadly taken from us far too soon. He loved life and lived it to the fullest. The unexpected tragedy has left all of us devastated.
‘He has left behind a family and fiancé who are shaken and heartbroken by his sudden loss, especially his two young beautiful sons Thomas and Peter who he absolutely adored.
‘He will be truly missed by his family and friends and everyone who knew him.
‘We would like to thank everyone for their kind words and support, it really is appreciated.’
The family of Mr Gething said: ‘Luke was a deeply loved son, brother, nephew, cousin and friend. He was kind, loving, caring, and hilarious.
‘He was a remarkable young lad who overcame so many difficult hurdles in his life. He was charming and kind to everyone who he knew.
‘He will be ever so missed by everyone that knew him.’
Officers are continuing to appeal for anyone who witnessed the collision, or saw the vehicle driving in the area prior to it.
The vehicle stopped at the BP and Marks & Spencer filling station on the A31 at Four Marks earlier that morning, before carrying on towards Winchester.
Anyone with information or who has dash cam is asked to contact police on 101, quoting 44190142001.