Alonso's return to Woking, seven years after he left following an acrimonious season as 2007 team mate to then-rookie Lewis Hamilton, had been an open secret for months in the paddock.
His partner next year had been far less clear-cut, with the former champions having to decide between one of their 2014 pairing of Button and Dane Kevin Magnussen, who will stay with the team as a reserve and test driver.
The decision to go with Button, who made his race debut in 2000 and was the most experienced driver on the starting grid this year, will see the Briton start his 16th season at the age of 35.
The former Honda driver remains McLaren's most recent race winner, having triumphed for the under-performing former champions in Brazil at the end of 2012.
McLaren have not won a race for two years and are going through a major overhaul, with changes at technical and managerial level.
They have also teamed up again with Honda in a repeat of their hugely successful partnership in the late 1980s and 1990s when Ayrton Senna and Alain Prost dominated Formula One.
Alonso, who won his title with Renault, has spent the last five seasons at Ferrari but his patience ran out after the Italian glamor team again failed to take the fight to dominant Mercedes this year.
The Spaniard is desperate to win a third title, something he came close to in 2007 when he and Hamilton finished level and one point behind Ferrari's champion Kimi Raikkonen.
"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," Alonso said.
"Over the past year I have received several offers, some of them really tempting 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 One scene for so long."
Button said he was extremely excited to be racing his sixth season for the team.
"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," he said.
"I am absolutely raring to go."
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