Christopher Colegate, 69, died after being found seriously injured in the road at the junction of Darby’s Lane and Heath Avenue in Poole on December 13.
Mr Colegate’s wife Freda and daughters Tash Motton and Rachel Hayward said they would never get over their loss but the driver coming forward would give them a small crumb of comfort.
The pensioner, who was frail, had a distinctive stoop and used two sticks, was walking along Darby’s Lane towards Oakdale Conservative Club when he was struck by a vehicle.
Mr Colegate, from Poole, was taken to the town’s hospital but later died.
Ms Hayward said: “Words cannot convey how our family is feeling since the events of last Friday night.
“An innocent husband, dad and grandpa was taken from us in such a horrific way.
“Despite his chronic disabilities, our dad remained independent and as active as possible. He was well known in the community and would do anything for us, his family and friends.
“This has been reflected in the numerous expressions of condolence we have already received from friends and strangers alike.
“The driver could have gone to his aid; could have called for help but instead, thought only of themselves and selfishly fled the scene.”
Her sister added: “We would now appeal to that driver to come forward and contact the police.
“As hard as it is for our family, you also must be struggling to live with what you have done.”