Tombazis, sacked by Ferrari after nine years following their winless 2014 season, joins the back-of-the-grid team with immediate effect.
It is the latest in a series of changes as Manor try to improve their form.
The team finished last in 2015 but have secured Mercedes engines and recruited Dave Ryan, who spent 30 years at McLaren, as racing director.
Manor technical director John McQuilliam said Tombazis would "provide us with the strength to design and develop consistently competitive racing cars to help steer us towards our long-term ambitions".
Manor are still without a team principal following the resignation, at the end of last season, of founder John Booth and Graeme Lowdon, who was the team's president and sporting director.
The team have yet to announce any drivers for 2016.
Indonesian GP2 driver Rio Haryanto has been linked to the team and is reported to have secured £10m in backing from the Indonesian government.
Among the other contenders are former McLaren driver Kevin Magnussen, who is also in the frame to replace Pastor Maldonado at Renault, and Manor's 2015 drivers - Englishman Will Stevens, American Alexander Rossi and Spaniard Roberto Merhi.
The team went out of business as Marussia at the end of 2014 but were rescued by Stephen Fitzpatrick, the boss of the energy firm Ovo.
Manor have signed former Ferrari chief designer Nikolas Tombazis as chief aerodynamicist.