"You choose a club and a project because of the ambition, and I think that West Ham has everything to be one of the biggest clubs in London," Nasri told West Ham's website.
"Coming back to the most competitive league in the world, with a team full of ambition with a manager that I know. It's the best job in the world, and I'm really excited about it."
West Ham have the option to extend the 31-year-old's deal by a year, the club added.
Nasri's original six-month ban for a drip treatment that contravened World Anti-Doping Agency rules was increased to 18 months in August after an appeal by UEFA's ethics and disciplinary inspector.
Nasri played for Arsenal between 2008-2011 and joined City for a spell that included two league titles and a League Cup before he fell out of favour following the arrival of manager Pep Guardiola.
The former France international joined Spanish side Sevilla on a season-long loan in 2016 before sealing a permanent switch to Turkish side Antalyaspor, who he left in January by mutual consent.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Alison Williams)
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