George Robertson died in hospital after being hit by a vehicle while walking between Bathgate and Torphichen on the A792 on Sunday, September 20.
His brother, David, has said that after much soul searching, the family has decided to put up the reward.
He said: “This reward is very reluctantly offered, it’s the last throw of the dice for us.
"My mum in particular didn’t like the idea of someone profiting from the death of her son.
"We put it on Facebook last night and it’s already got over 3,500 shares all over the UK.
"From Argyll and Bute to London, and I can’t thank people enough for their kind words.”
The police have run social media campaigns as well as TV appeals that have so far, yielded no information.
They believe that the car involved in the incident was a dark coloured Nissan Qashqai.
David continued: “The police have checked over 300 Nissan Qashqai’s in the area.
“They’ve been really involved, checking CCTV and going round houses to see if they have CCTV, or even those doorbells with the cameras that record the driveway just to see if they can catch the car.
"Because of the light, they can’t get the registration number.”
The family hope that the reward will tempt those who have information, but are possible too frightened to come forward.
When they made the decision to put forward a reward, many of their friends offered to donate.
David explained: “The reward is an awful lot of money from me, my mum and my brother in America.
"We refused donations because of the time of year, it didn’t seem fair to take money off people.”
George was 53-years-old when he tragically died, and left behind a wife and two young children.
His brother concluded: “Catching whoever did this won’t bring George back, but it will stop them from doing it again.
"The family need some sort of closure.
"George was young and fit, we still can’t get our heads around it.”
Anyone with information can contact Police Scotland through 101, quoting incident number 4127 of Sunday, September 20.