And Button said he was relishing the prospect of working with - and against - his new team-mate.
"I think we're all up for challenge," said Button.
"He knows what I've achieved, and what he's achieved in his short career is very special.
"He's an exceptional talent, so it's not going to be easy for me or for him but we've started thinking about 2010 and how we can work together.
"I've achieved what I wanted to do in this sport, my first goal, which was to be world champion - now for myself I want to race against him and work with him.
"Together we'll be a tough team to beat."
Button spent seven years with his former team in their various incarnations before winning the world title at the age of 29 in the team's first season as Brawn.
Brawn only came into being a year ago when Honda pulled out, but enjoyed a remarkable debut season, claiming both the drivers' and constructors' titles.
And Button admitted it would have been hard to recapture the thrill of that first season if he had stayed.
"Not many people are ever in that position that I found myself in," he said.
"At the end of 2008 I was excited about 2009 with Honda but that ended on 5 December and I was lost - I didn't know where I'd be racing.
"When I jumped into the Brawn car in March and realised we had a monster, it was a special feeling for the whole team after what we'd been through. I'm not sure if that emotion will ever be there again."
And when he finally reached the summit, it was not long before Button felt he needed to move on to pastures new.
"After winning the championship it was a strange feeling - I was happy for myself and for the people who'd helped me along the way, but immediately it was 'what happens for me now I've achieved my initial dream?'
"After a couple of days I realised I needed a new challenge," said button.
"Where I'm going to be next year, and who I'm going to be with, I know it'll be a big challenge.
"It's so exciting for me knowing that I'm heading into a season and it'll be a proper fight - it won't be easy, I know that.
"The last seven years I've been with Brawn, Honda and British American Racing - it's pretty much the same team - I had a big family around me.
"I was in a comfort zone, and coming to McLaren, I won't have that - it's something I need to work on but it's part of the buzz of the new challenge."
Brawn have now been renamed Mercedes Grand Prix and have already signed German Nico Rosberg as one of their drivers, with his compatriot Nick Heidfeld the favourite for the second seat.
With the usual close-season merry-go-round of drivers moving teams, other teams being renamed and brand new ones being thrown into the mix, Button said 2010 had all the makings of a fascinating season.
"I don't know anything - nobody really knows what will happen in 2010 which is why it's so exciting," he said.
"I think 2010 will one of the most competitive seasons we've seen in a long time."
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