The Briton, the most experienced driver on the starting grid and 35 years old next January, will partner Spaniard Fernando Alonso in a lineup of champions.
Out of contract at the end of the season, the 2009 champion had spent the last few months wondering if he had a future in the sport but finally signed a contract on Wednesday evening.
"Fernando was talking about (McLaren group head) Ron (Dennis) and himself being in a hotel room many times over the past few weeks. I had that last night," Button told Reuters Television.
"An hour and a half of just running through everything, just getting a lot of stuff out in the open really between us. It was a good thing to do. I feel a lot more comfortable afterwards which is great.
"I have had a long career in Formula One but this feels like a new start. I spoke to one of my sisters this morning and she said, 'I've got goose bumps like it is your first drive in F1' and for me it is the same but with 15 years experience."
The Button/Alonso pairing gives McLaren the oldest lineup on the starting grid, with a combined experience of more than 500 races.
Alonso will be the third world champion Button has had as a team mate, after Canadian Jacques Villeneuve and his own compatriot Lewis Hamilton, and potentially the toughest.
"I feel we bring a lot to this team working together," he said. "I think we are both grown up, intelligent (enough) to understand that we have to work closely together and you do your talking out on the circuit, that's the way it has to be."
Button said it was also important that his new contract was for more than just a year.
"This is a new project, an exciting project," he said. "To be part of the legendary partnership between McLaren and Honda is not a one-year thing... it is not something I am doing just to be around for one year."
(Reporting by Alan Baldwin, editing by Ken Ferris)
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