Webber has confirmed stickers bearing Wheldon's logo, his initials in red, white and black, have been manufactured to place on his helmet, that of Button and any other wishing to pay their last respects.
Button has also revealed he will wear a black armband in Sunday's inaugural Indian Grand Prix for Wheldon, who was killed in an Indy 300 race in Las Vegas 11 days ago.
"I sent Jenson a text after the race in Korea and I told him I wanted to get some stickers made up for our helmets," said Webber.
"I asked him if he was keen and he said he was. It's a nice little sticker because we both knew him. It's only natural he is part of us a little this weekend."
Webber initially got to know Wheldon in the mid-1990s when they were instructors at a racing school in Brands Hatch.
As for Button, he raced against Wheldon in karts from 1989-1994, and again in the Formula Ford championship in 1998.
For Button, Wheldon served as an inspiration as he said: "I've so many memories of racing with Dan.
"When I was nine years old we were competing and he had the big number one on his car as the British (kart) champion.
"It was Dan, myself and Anthony (Davidson) that pretty much won everything in kadet racing.
"But he was the guy I was always trying to beat, the one I was motivated to get out of bed for and fight against.
"His is a massive loss to motorsport, but you have to take the good memories from it and look at what he achieved in his life that most people wouldn't achieve if they died in their 70s or 80s.
"It's a very tough time for everyone that knows him and is close to him."
With regard to his planned tribute, Button said: "I don't think I will be alone, there will be a few drivers.
"It's a tough one because how much can you do? It's always tricky, but he will definitely be in our thoughts this weekend when we are racing."
Motor sport was further rocked at the weekend by the death of Marco Simoncelli following a crash in the Malaysian MotoGP.
For Webber, a bike fan at heart, the loss of the flamboyant Italian adds further poignancy to the Australian's weekend.
"In a way motorbikes are even dearer to my heart than car racing because I started out in bikes," said Webber.
"I was watching the race live and when you see it you just hope it is not real, particularly for a guy of such a young age.
"He was a phenomenal character who will be massively missed, no question about it."
But despite two such tragic incidents in the space of a week, for Webber, they do not alter his mindset.
"I've had moments in my career where it's been close for me," said the 35-year-old.
"You know when you step into the car you are doing something where you are putting yourself at risk.
"It's always going to be there because you're competing at speed, against other people, and there might be an error of judgment or because of the weather, then you might get hurt.
"That's the way it is. But in driving the car tomorrow I will feel incredibly safe and comfortable to push it as hard as I can."
Webber's views have been echoed by all the F1 drivers, who see it as very much a case of 'life goes on'.
That was a point noted by seven-times champion Michael Schumacher who said: "If, when you are on top something happens, then that's what I would call fate, and fate is something we all have to face sooner or later.
"I'm certainly very much touched by what has happened for both of the drivers we have lost, but unfortunately you have to say that's life."
One driver understood to be mulling over his options is three-times IndyCar champion Dario Franchitti, cousin of Force India's Paul di Resta.
Di Resta said: "It's hurt him. Dan was a very close friend.
"I know Dario is out testing the new car at Sebring (Florida) this week and he has said in interviews it has made him think.
"Only time will tell. If he wants to continue we'll support that decision."