The announcement comes in contrast to previous reports that British veteran Button would leave the team in favour of Danish rookie Kevin Magnussen.
However, the 34-year-old will be given one more season in a McLaren at least, with Honda coming on board as engine provider for 2015, with Magnussen kept on as test and reserve driver.
Button - the 2009 world champion - has been with McLaren since 2010 and is looking forward to partnering another former champion in Alonso.
"I am extremely excited to be embarking on my 16th year in Formula 1 and my sixth season for McLaren," he said
"Like Fernando, I am certain that McLaren and Honda will achieve great things together, and I feel sure that, working together, all of us will pull incredibly hard to create a brilliantly effective winning team.
"Being a part of new-look McLaren-Honda is a wonderful opportunity for all of us, and I am very pleased to have been invited to do my bit. In fact, I am absolutely raring to go.
"I am also very glad that Kevin will remain part of the team. He is a very quick driver and a really nice guy.
"Last but far from least, I am very much looking forward to having a driver as fast and as experienced as Fernando as my team-mate. I am sure we will work extremely well together."
Alonso returns to McLaren after an acrimonious departure in 2007 in which Alonso claimed then-colleague Lewis Hamilton was favoured due to being English.
But the Spaniard envisages no such issues this time around.
He said: "I am joining this project with enormous enthusiasm and determination, knowing that it may require some time to achieve the results we are aiming for, which is no problem for me.
"Over the past year I have received several offers, some of them really tempting, given the current performance of some of the teams that showed interest.
"But, more than a year ago, McLaren-Honda contacted me and asked me to take part, in a very active way, in the return of their partnership – a partnership that dominated the Formula 1 scene for so long.
"McLaren-Honda's repeated and open desire, perseverance and determination in making it possible for me to join their exciting renewed partnership, have been some of the main factors that made me take this decision."