It will be the first multi-million pound A-list film to get made at the new facilities on the outskirts of the Welsh capital.
The original film starred Brandon Lee, who died on set after being accidentally shot.
Carwyn Jones made the announcement while visiting the studios as Pinewood marks its first year in Wales.
The new film will draw on the Welsh government's Â£30m Media Investment Budget - which has already been used to help fund the film Take Down.
But a reboot of The Crow is a real feather in cap for the new studio, as the original remains highly regarded with passionate fans.
It began life as a dark fantasy action comic book story, in which rock musician Eric Draven is revived from the dead to avenge his murder and death of his girlfriend.
The original film spawned a number of sequels and a television series.
Actor Jack Huston is widely reported to be in talks to take on the lead role, after earlier speculation that Welsh actor and The Hobbit star Luke Evans might take the part.
The studio confirmed that The Crow "will begin filming at Pinewood shortly".
"It will be first major feature film production to be shot at the studio," said the company.
Touring the facilities at Wentloog on Monday, First Minister Carwyn Jones said: "The fact Pinewood has chosen to open a facility in Wales and so many production companies are filming here is testament to our beautiful landscape, vibrant cities, wonderful historical assets."
He said alongside a skilled workforce and Welsh government support "these combine to make our nation an excellent place to produce high quality film and television".
The studios are already committed to another major production - an historical drama for the US cable channel FX.
Cult 90s film The Crow will be remade at the Pinewood Studios in Cardiff, the first minister has announced.