The team, which was rescued from being place under administration by Canadian billionaire Lance Stroll and a consortium of investors, was accepted as an entry to the Formula One world championship by the ruling body.
Founded and co-owned by Indian businessman Vijay Mallya, Force India was put into administration in the UK on 27 July.
The team’s confirmation as a new entity, however, means that it will start from zero without inheriting any of the constructors’ championship points scored by Force India.
Drivers Mexican Sergio Perez and Frenchman Esteban Ocon will keep their individual points scored in the drivers' championship.
The original Force India team was sixth in the standings with 59 points, having finished the last two seasons in fourth position.
“We are all passionate about motor racing. We recognise the racers' spirit in Force India and we are extremely motivated to make this team even more special in the years ahead,” Stroll said.
FIA president Jean Todt said he welcomed the resolution of Force India difficulties and the continuation of a 10-team championship.
The repbaptised team announced also that former chief operating officer Otmar Szafnauer will become the team principal and chief executive officer.