The English duo have driven the circuit on the McLaren simulator and are looking forward to a return to the US on the Formula 1 calendar for the first time in five years.
Button tweeted: "Good couple of days at the [McLaren Training Centre], yesterday driving the simulator for Sao Paolo and Austin and I must say Austin is Epic!!"
Hamilton, who won the last US GP in Indianapolis in 2007, added: "I have to admit, I'm absolutely made-up that we're going back to the States.
"It's a fantastic country and a place where our sport truly deserves to be. I think the Circuit of the Americas looks like it could also be the place that modern Formula 1 finally calls home."
The Circuit of the Americas has been designed to incorporate elements from tracks across the world into one fluid lap.