The 2009 World Champion will become just the fifth driver to reach the milestone when he takes his place on the grid in Bahrain on Sunday, joining Rubens Barrichello, Michael Schumacher, Ricardo Patrese and Jarno Trulli.
Button is just eight races away from going third in the all-time list, and former McLaren team-mate Hamilton - now at Mercedes - stated his admiration for his compatriot.
"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," he said.
"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."
Button himself added: "For me being 14 years in the sport, I still feel I have more to learn. I'm definitely not the perfect driver yet, and I never will be, but there's always more to learn and that's something to me that's exciting about the sport."
Hamilton sits second in the drivers' championship after two races, while Button is two points further back in fourth.