"After careful consideration and evaluation we are certain this partnership with Honda is the right direction for the team," Red Bull Racing principal Christian Horner said in a statement announcing the deal for 2019 and 2020.
Red Bull won four drivers' and constructors' championships in a row with Sebastian Vettel, now at Ferrari, and Renault between 2010 and 2013.
The pairing also won 47 races before the current V6 turbo hybrid power units were introduced but Renault's struggles with the new format stretched the relationship to breaking point and the British-based team now brand their engines Tag Heuer.
Honda also had their difficulties, switching to Red Bull's junior team Toro Rosso this season after a failed three-year partnership with McLaren ended in mutual recrimination.
McLaren now use Renault power units, but their car has still under-performed Red Bull.
Red Bull's decision to switch to the Japanese manufacturer means their two teams now have exclusive use of Honda engines but could complicate efforts to retain Australian Daniel Ricciardo.
Ricciardo, 28, has won twice this season but is out of contract at the end of 2018 while 20-year-old Dutch team mate Max Verstappen has a long-term deal.
Horner hoped Honda could take Red Bull back to the top.
"We have always taken decisions such as this dispassionately and with only one criteria in mind -- do we believe the outcome will allow us to compete at a higher level," he said.
"We have been impressed by Honda's commitment to F1, by the rapid steps they have made in recent times with our sister team Scuderia Toro Rosso, and by the scope of their ambition, which matches our own."
The team's official name will remain Aston Martin Red Bull Racing.
Honda president Takahiro Hachigo said the deal would give the manufacturer access to twice as much data.
"Discussions proceeded very quickly, thanks to Red Bull's open and respectful attitude towards Honda, leading to a deal that is fair and equitable for all parties," he added.
Renault acknowledged the decision in a statement as "a natural evolution" for both parties.
The French carmaker, which will now have only the works Renault team and McLaren using its engines, had wanted a decision before this weekend's French Grand Prix at Le Castellet.
(Reporting by Alan Baldwin; Editing by John O'Brien)
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