Hamilton said that the sport does not get easier with age, and is impressed with the way that the McLaren driver can keep coming back strongly each year.
"I have a huge amount of respect for Jenson, watching him come back every year, to have that motivation, because as you get older it gets harder," Hamilton is quoted as saying by Sky Sports News.
"It gets harder to train, even for younger people, and every year it gets harder and harder to challenge, and how you spend your energy is different every year. Yet every year he is on it, focused, and especially this year as his dad's not with him, who has been with him all these years.
"Even so, he is still there, still working away, and I take my hat off to him. He's a great athlete. I can only hope and dream I get to have as long and as successful a career as he has had."
By the end of the season Button should become the driver with the third-highest number of races in Formula 1.