The announcement follows weeks of speculation over whether Button, world champion with Brawn in 2009, or rookie Dane, Kevin Magnussen, would be retained to team up with Alonso, who returns to the team from Ferrari.
"I am extremely excited to be embarking on my 16th year in Formula One and my sixth season for McLaren," said Button in a statement on the McLaren website.
"Like Alonso, I’m 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 combination."
McLaren chief executive officer Ron Dennis took his time before plumping for Button over 22-year-old Magnussen, having held a meeting with board members to discuss the matter last Thursday.
Magnussen finished in 11th place in the drivers' championship in his maiden campaign, three places behind Button. He will remain at McLaren as test and reserve driver.
Alonso, world champion with Renault in 2005 and 2006, spent the 2007 season at McLaren before returning to Renault. After two years at Renault, he moved to Ferrari.
But Ferrari failed to compete with the dominant Mercedes team last season, with Alonso finishing 223 points behind champion Lewis Hamilton in sixth place.
"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,” said the 33-year-old Spaniard.
"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."
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