England fly-half Wilkinson's 12-point haul in England's quarter-final victory over Australia on Saturday took him past Scotland legend Hastings' career total of 227 World Cup points, which was achieved from 1987 to 1995.
England's 2003 World Cup final hero now has 234 points to his name, and will be looking to add more in the semi-final against France on Saturday.
Hastings, who is now chairman of Edinburgh, said: "Jonny Wilkinson is a pretty decent player to have broken my record and I'm pleased for him.
"I suppose it was always inevitable that somebody would break my record at some stage."
He added: "I'm proud that my record lasted three World Cups and who knows how long his will last?
"He is raising the bar for someone else to overtake that total and I'm sure at one point someone will eventually do that."
Hastings paid tribute to Wilkinson for overcoming a catalogue of injuries since the last World Cup to make a telling contribution this time.
"I think he has had a very difficult time since the last World Cup," said the 45-year-old.
"So for him to not only have a World Cup winner's medal, but also the most points is great. He is now setting a new target for somebody else to break."