The deal was announced by both sides on Sunday at the Russian Grand Prix. No details about the cost or duration were given, although it is likely to be until 2020 at least.
Honda currently has an exclusive agreement with former world champions McLaren but that relationship, which started in 2015, has been strained due to a lack of engine performance and reliability.
Sauber, a long-standing mid-table team who are languishing near the back of the field after fighting back from a period of financial difficulties, are using last season's Ferrari engines at present.
Neither they, nor McLaren, have scored a point so far in three races this year.
"In addition to the partnership with McLaren which began in 2015, Honda will begin supplying power units to Sauber as a customer team starting from next year," said Katsuhide Moriyama, Honda's head of brand and communication operations.
"This will be a new challenge in Honda’s F1 activities," added the executive in a statement.
"In order to leverage the benefits of supplying to two teams to the maximum extent, we will strengthen the systems and capabilities of both of our two development operations, namely HRD Sakura and the operation in Milton Keynes."
Under Formula One rules designed to ensure no team is left without an engine supply, manufacturers are obliged to supply a team if they have spare capacity and are asked to.
Champions Mercedes currently supply three of the 10 teams, as do Renault and Ferrari, while Honda have only one partner.
The Japanese manufacturer is still hoping to make big strides in the latter part of the season, with Mercedes and Ferrari enjoying a big power advantage over the others.
Sauber principal Monisha Kaltenborn said the deal was part of the team's realignment and recovery as it celebrates its 25th anniversary in Formula One.
"We have set another milestone with this new engine era, which we await with huge excitement and of course we are looking for new opportunities," she said in a statement.
"We very much look forward to our partnership with Honda, which sets the course for a successful future -- from a strategic as well as from a technological perspective."
(Reporting by Alan Baldwin, editing by Amlan Chakraborty)
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