The Microsoft branding appears on the sides of the mostly silver and black car's airbox and front wing.
No financial details were given, although Sky News cited an unnamed sponsorship expert as suggesting the deal could be worth $60 million a year for the team.
The team will start testing in Barcelona next week amid widespread speculation that they have found a loophole in the new engine regulations that could put them ahead of rivals Ferrari. Mercedes also provide power units to McLaren, Williams and Renault-owned Alpine as well as their factory team.
The team will hold an online launch event on February 2 with two more tests in Bahrain before the season starts in Australia on March 8.
It was also announced separately that 22-year-old French driver Doriane Pin, winner of last year's all-female F1 Academy series, would step up to a development role with the team this season.
Pin will work in the simulator, have additional duties at the factory and attend several grands prix trackside, the team said.
Mercedes finished second to champions McLaren last season, with British driver George Russell taking two wins and Italian rookie Kimi Antonelli stepping on the podium three times and becoming the youngest driver to set a fastest lap.
The team won eight constructors' titles in a row between 2014 and 2021 before Red Bull and then McLaren became the teams to beat.