Honda chief executive Takanobu Ito and McLaren team principal Martin Whitmarsh made the announcement in Tokyo.
The Japanese manufacturing giant quit the sport at the end of 2008 at the height of the global financial crisis.
But with F1 due for a major engine overhaul from next season when turbo-charged 1.6-litre V6 powerplants replace the current 2.4-litre V8 units, Honda has decided the time is right to make a comeback.
McLaren and Honda formed one of the most successful partnerships in F1 history from 1988 to 1992, winning 44 grands prix and eight world titles in such a short period of time.
It will bring to end McLaren's long-running engine deal with Mercedes that began in 1995, so far yielding 78 victories, one constructors' and three drivers' championships.
Although Honda had little success with their own team for three years after branching out from 2006-08, their return is seen as something of a coup for McLaren.
Whitmarsh said: "I am delighted to announce Honda and McLaren will soon begin a new chapter of our legendary Formula One partnership.
"It is a partnership synonymous with success. Together, in 1988, we created the most successful Formula One car of all time which was driven to victory 15 times out of 16 (grands prix) by Ayrton Senna and Alain Prost.
"McLaren and Honda are about to embark on a new and extremely exciting adventure together.
"For everyone who works for both companies, the weight of our past achievements lies heavily on our shoulders.
"But like McLaren, Honda is a company with motor racing in its blood and its the mark of ambition we both share that we want to re-create past glories and take McLaren-Honda back to the top.
"Together we'll form a lasting partnership to deliver success on the track, backed up by world-leading R&D (research and development) and engineering intelligence."
Whitmarsh concedes the two companies have "embarked on a very demanding journey", but has no doubt it will ultimately again prove successful.
"Formula One is a hugely challenging sport and is becoming more competitive every year, but we're both totally committed to the success of our partnership and to our ultimate goal - to win," added Whitmarsh.
"That commitment, combined with our world-beating engineering know-how, gives us the confidence we can overcome the challenges we face.
"Together, Honda and McLaren have a great legacy. We formed a uniquely successful partnership that took on and beat the world.
"Together, we created some of the greatest, most-iconic Formula One moments of all time, which are still being talked about today all around the world.
"As we look to the future, both Honda and McLaren are utterly committed to maintaining that legacy and being successful once more."
Jenson Button, who spent six years working with Honda cars or engines from 2003-2008, said: "I know exactly how passionate Honda is about motorsport, and Formula One in particular.
"I grew up watching McLaren-Honda Formula One cars racing and winning around the world - they wrote their own glorious chapter of Formula One history.
"Even now, picturing those unmistakable red-and-white cars evokes vivid memories of some of the most dramatic and exciting motor racing the world has ever seen.
"McLaren-Honda: I know how much passion, success and pride are encapsulated within just those two words.
"That's why I'm so thrilled and excited about what's not only a fantastic opportunity for the team, but also a great development for Formula One fans and the sport as a whole."