Price won his maiden PDC World Darts Championship on Sunday evening, pocketing £500,000 by doing so.
Price has been the most successful player on the PDC circuit this season, and has now taken the world No.1 spot for the first time.
The Welshman rises to the top in place of Van Gerwen, who was knocked out at the quarter-final stage by Dave Chisnall.
Price had said of the race to No.1: “I’m going to get plenty of opportunities, I’d love to be No.1.
“I’d love to be world champion and I’m sure there’s not many times you’re going to get to a final.
“I’ll try to grasp it with both hands, and if it happens it happens. If not I’ve had a really good year already.”
Price played professional rugby union before switching to darts and scored a try for Cross Keys as they won the 2012 SWALEC Cup at the Millennium Stadium.
Price said: “Eight years down the line, it’s crazy to have a completely different career.
“I never thought anything in sport would top that feeling, but the possibility of winning a darts world championship and becoming No. 1 in the world would be incredible.
“That would give me a similar sort of buzz, but I never dreamed it would be possible. But it is a lot more money on take.
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“I hadn’t even picked up a dart when Cross Keys won that rugby final in 2012.
“It would be special to replicate that feeling in another sport. It’s not the end of the world if I come up short, but there can’t be many people out there who have won a major rugby cup and a darts world champion.
“Do I dream about being No.1 in the world? Yes, every day – who wouldn’t?”