Nasri has been omitted from the Gunners squad travelling to Italy for Wednesday's Champions league play-off second leg against Udinese.
"Arsenal can confirm that they have agreed terms for Samir Nasri to move to Manchester City," Arsenal said in a statement on their official website, adding that Nasri was on his way to Manchester for a medical on Tuesday afternoon.
Nasri is set to become the second key Arsenal player to leave the club this month after Barcelona signed captain Cesc Fabregas for a reported fee of around €40 million.
City had already laid out around £50 million in this summer's transfer window on Argentina forward Sergio Aguero, French left-back Gael Clichy - also bought from Arsenal - and Montenegro defender Stefan Savic.
Since being taken over by the Abu Dhabi United Group in August 2008, City have spent an unprecedented amount for British football on buying top players.
In 2009, they bought Carlos Tevez, Gareth Barry and Emmanuel Adebayor. During the August 2010 transfer window their outlay was around 130 million on players such as Yaya Toure, David Silva and Mario Balotelli.
Under Roberto Mancini, who took over as manager in late 2009, City finished third in the Premier League last season, one place above Arsenal. City also won the FA Cup, their first major trophy in 35 years.
Arsenal manager Arsene Wenger is under increasing pressure from fans to buy a big-name player to replace Fabregas and Nasri, and to end the club's six-year trophy drought.
Arsenal lead Udinese 1-0 after the first leg of their Champions League play-off. City qualified directly for the group stages of the competition.
