Two-time Indianapolis 500 winner Wheldon, who died from injuries suffered in a crash at Las Vegas Motor Speedway in October, was awarded a posthumous lifetime achievement honour at the Autosport British Racing Drivers' Club awards.
Button was a friend and competitor of Wheldon since childhood and said: "We grew up together and had so many great experiences together, it's an era of drivers that have gone on to achieve a lot.
"Most of the time you couldn't beat him, when you did it really did mean a lot. He's the guy you'd get out of bed to race.
"He was a fun guy, he loved his racing, he worked hard but he also played hard, that's the way you've got to go through life if you have that possibility.
"The early days were great, but Formula Ford was also very special - the first year of kart racing together and we had a lot of good fights that season."
Wheldon, from Olney in Buckinghamshire, achieved stardom in the United States where he won the IndyCar Series - and its signature race - in 2005 and repeated his success at Indianapolis this year.
And Button noted: "The competition there is fierce and to come in and win the Indy 500 like he did, and the championship, and also to win the Indy 500 this year, first race in 2011, it's phenomenal, you don't see that very often."
Another British driver to enjoy success Stateside, Scotland's Dario Franchitti, joins Button at a kart racing event to remember Wheldon and Button was delighted to see such a gathering of stars.
"It's absolutely freezing but it's a great turnout tonight, it's great to see so many racing drivers from different formulas around the world," he said.
"Dario's here as well, who was one of Dan's closest friends and closest rivals, so it's a great turnout and I'm very happy to be here, it's great to be a part of it."