The unnamed film will be in addition to the forthcoming Star Wars trilogy, the first instalment of which will be directed by JJ Abrams.
Writer Gary Whitta, who penned the script for 2010?s The Book of Eli, will write the screenplay for Edwards’ film.
The film is due to be released on 16 December 2016.
In a statement, Edwards said: “Ever since I saw Star Wars I knew exactly what I wanted to do for the rest of my life – join the Rebel Alliance!
“I could not be more excited and honoured to go on this mission.”
Whitta echoed his sentiments and said the “opportunity to contribute” was “literally a dream come true”.
Box office success
Edwards’ recent 3D film Godzilla topped the US box office chart and has taken more than $216m (£128m) worldwide, according to Boxofficemojo.
He also won widespread acclaim for his independent film Monsters, which was released in 2010.
The original Star Wars trilogy – which consists of the original film in 1977, 1980?s The Empire Strikes Back and 1983?s Return of the Jedi – was always envisaged by creator George Lucas as the central chunk of a nine-movie cycle.
The films followed the fortunes of young hero Luke Skywalker, cocky pilot Han Solo and the feisty Princess Leia as they battled against the Galactic Empire.
A trilogy of Star Wars prequels – 1999?s The Phantom Menace, 2002?s Attack of the Clones and 2005?s Revenge of the Sith – followed.
Disney – which announced it had bought Lucasfilm for $4.05bn (£2.5bn) in 2012 – has previously said Lucas would remain as a creative consultant on the forthcoming trilogy, which begins with Star Wars: Episode VII, due to be released next year.