It is expected that Button will announce his retirement from F1 at this week's Japanese Grand Prix, bringing to an end a 16-year career that included a World Championship title in 2009.
The Briton is a popular figure both in the paddock and with fans, and Watson has admitted that his exit would leave a void.
"He is a human face to a paddock which is a bit anodyne nowadays. The paddock will be poorer without him," Watson told Sky Sports.
For Watson, Button represents a rare breed of racer who has been able to compete at the top of the field while maintaining a friendly, professional demeanour off it.
"He'll be remembered for being a nice bloke and for genuinely being quick - the two don't normally go together," said Watson.
"He has been a pleasure to work with from the media's point of view. He has always been a smiley face during the good times and bad, he's been a great advocate of the sport and he will be missed by a lot of people - the fans still like him, the people at McLaren still like him. He has brought the sport a lot."
David Coulthard has echoed Watson's sentiments, calling Button one of F1's true stars.
"Button is, without doubt, still delivering behind the wheel and equally he is an asset to McLaren and to the sport itself," Coulthard wrote in his BBC column.
"He is one of F1's main stars - one of only a handful of drivers who, when they walk through an airport or other public place, will be recognised.
"Losing him would leave a void in F1 before another star emerged to replace him alongside drivers such as Alonso, Lewis Hamilton and Sebastian Vettel."
The Scott added: "I just hope that, if he has decided to go, he gets a chance to be celebrated and clapped off the stage at the end of his career.
"A driver and man of his calibre deserves to be sent off with a standing ovation, not slope off into a winter of uncertainty."
Button made his F1 debut for Williams at the 2000 Australian Grand Prix, and has gone on to make 278 starts, registering 50 podium finishes and 15 race wins, while claiming the World title in 2009.