The crowd chanted Waddell's name during the final and afterwards Taylor was presented with the new trophy, which has been named for the popular commentator who died from cancer last summer.
"I'm the proudest man in the world at the moment," said Taylor, who received a winner's cheque for £200,000.
"There was a 180 when the crowd were singing Sid Waddell's name and I looked up and thought he'd put that in for me.
"I'm world champion again and I'm so happy."
He added: "Sid was like a father figure to me - he was my biggest fan, Sid was. I loved him to bits. I am absolutely over the moon. It's the biggest night of my life."
Dutchman Van Gerwen threw a nine-dart finish on the way to beating James Wade 6-4 in his semi-final and again showed his class in a contest he entered as favourite.
But 52-year-old Taylor, who secured his passage to the final with a victory over Raymond van Barneveld, showed his class on the big points as he turned a 4-3 deficit into a 5-4 lead.
Taylor made his move at the crucial moment at 2-2 in the ninth, a 132 teeing up a double-top finish for a break, which he duly completed after Van Gerwen had choked on a 107 checkout chance.
Van Gerwen looked shaky in the next set as Taylor raced to a 2-0 lead, the Englishman eventually prevailing 3-1 to take a 6-4 lead.
The nerves of both men told at 1-1 in the next set as they took turns to spurn easy checkouts, but when Taylor landed a double nine to move into a 2-1 lead the writing was on the wall for Van Gerwen.
Taylor duly wrapped things up on a double 16 to clinch his first title since 2010, much to the delight of the raucous London crowd.
Taylor hinted ahead of the match that he was toying with the idea of retirement, but indicated that he may bid for a 17th title next year.
He said: "I'm 53 next year and I'm coming back to defend a world title. It's ridiculous really."