Hamilton and Button were partners at McLaren between 2010 and 2012 before the former switched his allegiance to Mercedes and claimed back-to-back world titles in 2014 and 2015.
Button remained with McLaren and is currently in his seventh campaign with the Woking-based marque but has opted to take a rest next year to recharge his batteries after 17 years of racing in Formula One.
The Somerset-born flyer claimed the World Championship title in 2009 while driving for Brawn but has not been competitive in recent years, with his last Grand Prix success coming in Brazil back in 2012.
The 36-year-old has hinted that he might return to the track in 2018 but there is a groundswell of opinion that his time in F1 might be over.
Whatever happens, fellow Englishman Hamilton is clearly a big fan and wishes Button well for his future plans.
"He's been a great driver for many, many years. A great asset to Formula One, he's contributed a lot," he said. "I remember sitting at home watching him in his first Grand Prix, I was still in high school hoping one day that would be me and it's kind of crazy now that we are both here.
"He will be missed but one day all you guys will be gone and somebody else will take your spot, same with me and life will move on. It's just the way it is."