In a simultaneous announcement, Jordan announced that they have extended their contract with Mugen-Honda until the end of 2001.
Honda, who withdrew from Formula One in 1992 after championship-winning alliances with Williams and McLaren, had planned to return to grand prix racing with their own team, but they have decided to pool their resources with BAR and maintain their partnership, through Mugen, with Jordan.
BAR's managing director, Craig Pollock, who had to pay compensation to Supertec for the cancellation of their contract at the end of this year, said: "It is very exciting news that Honda has decided to return to grand prix racing as a partner with the British American Racing team.
"It is a company with an illustrious heritage in motor sport and you can be sure that, together, British American Racing and Honda will be aiming to add more stories of success to the Formula One history books in the years to come."
Honda will design and develop engines of equal specification to be supplied through Mugen to Jordan, who are third in the constructors' championship behind Ferrari and McLaren-Mercedes.
The Jordan team owner, Eddie Jordan, said: "As our current position in the championship demonstrates, we have developed an excellent relationship with Mugen-Honda. The combined support of Honda and Mugen with an equal status engine supply until the end of 2001 now gives the team the stability it requires to mount an even stronger world championship challenge."
Honda helped Nelson Piquet, Alain Prost and Ayrton Senna to the drivers' titles. The company dominated the sport from 1986 to 1991, winning two constructors' titles with Williams, then four in a row with McLaren before slumping sales forced their withdrawal.
Honda originally planned to return as a constructor in its own right and were extensively testing until only last month when their project leader, Harvey Postlethwaite, died during a session in Barcelona.