Button's future had been the subject of intense debate and scrutiny in recent weeks as rumours swirled that he might call time on his F1 career. The Briton admitted it hadn't been a straightforward decision, but said recent talks had convinced him to stay with the team.
"Over the past month or so I have done quite a lot of thinking, and it is no secret that I was at one point in two minds about my future,” Button said.
"But I have been a McLaren driver for six seasons now, and in that time I have got to know Ron [Dennis, McLaren chairman and chief executive] very well. He and I have had some very good chats these past few weeks, and during those chats it has become clear to me that Ron is both utterly determined and uniquely equipped to lead our team through its current difficulties to great successes in the future.
"That gives me great confidence, and it is for that reason that, together, he and I have decided to continue our partnership; and, as soon as I had made that decision, straight away I realised it was the correct one.
"Okay, granted, this year has not been an easy one for us, but we know what we need to do to improve things and, in collaboration with Honda, we will work extremely hard over the next weeks and months in order to make sure that 2016 will be a much better season than 2015 has been. I can't wait!"
Dennis said retaining a man of Button's experience and talent was a massive boost to the team.
"Jenson and I have been discussing his plans in private for the past few weeks, and the fact that our talks have led to today's announcement is very pleasing to both of us and will delight and motivate all at McLaren-Honda,” he explained.
"As I have made clear whenever I have been asked about the subject, Jenson's current contract is of two years' duration [2015 and 2016]. There is a 'terminate after year one' option that McLaren could have triggered if we had wished to do so, but, once it became clear from my many conversations with Jenson that he remained as enthusiastic and as committed and as focused as ever, that option immediately became an irrelevance.
"That being the case, Jenson will race for McLaren-Honda next year, under the terms and conditions as set out in the two-year contract that both parties entered into a year ago.
"As I say, I am extremely pleased. Jenson is the most experienced driver currently racing in Formula One, and next season he is due to become only the third driver [after Rubens Barrichello and Michael Schumacher] in Formula One history to pass the milestone of 300 Grands Prix.
"But, although that wealth of experience makes him a massively valuable asset to our team, hugely expert in all aspects of the 21st-century Formula One driver's craft, he is also supremely fit and as super-fast as ever."
Button, already the third most experienced driver in F1 history, is therefore set to make his 300th Grand Prix start next year in Malaysia. Only Rubens Barrichello (322) and Michael Schumacher (306) have contested more.