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.
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.
Alonso, who won his title with Renault, has spent the last five seasons at Ferrari but his patience ran out after the Italian glamour 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.
Image: Fernando Alonso of Spain and Ferrari and Jenson Button of Great Britain and McLaren during the drivers' press conference ahead of the Abu Dhabi Formula One Grand Prix at Yas Marina Circuit on November 20, 2014.
Photograph: Clive Mason/Getty Images
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