Chilton, 24, drove for two seasons in F1 with Marussia before losing his seat in 2015 after the team was re-branded as Manor Marussia.
He competed in Le Mans 24 Hours in 2015 and last season raced in America's Indy Lights series, winning once.
Chilton said: "In the last three years I haven't had a car that can get a podium. This year I have no excuses."
New Zealander Scott Dixon won last year's IndyCar drivers' championship with Chip Ganassi.
Chilton, who will drive a Chevrolet, will become the fourth British driver in the last 24 years, after Nigel Mansell, Mark Blundell and Justin Wilson, to join IndyCar full-time after competing in F1 in the same capacity.
Wilson died at the age of 37 after being struck by flying debris and suffering a serious head injury in an IndyCar race in Pennsylvania last August.
Chilton made 35 starts in F1 across the 2013 and 2014 seasons and set a new driver's record of 25 consecutive finishes, with 19 of them coming in his first season.
Former British Formula 1 driver Max Chilton will join Chip Ganassi Racing for the 2016 IndyCar season.