Bilic was without a club after leaving Chinese Super League side Beijing Guoan in January and has signed an 18-month contract at Vicarage Road.
Watford, relegated from the Premier League last season, parted company with Edwards after winning just three of their opening ten Championship games this season.
The club currently lie in 10th position on the Championship table.
Bilic's previous job in the championship saw him guide West Bromwich Albion to Premier League promotion in the 2019/2020 season.
In a statement, Watford owner Gino Pozzo said: "As with all decisions taken by the Board, I believe this change to be in the best interests of the club.
"We felt Rob had enough time to show us the identity of his team, however performances haven't reflected our hopes and ambitions.
"Now we must move forward, and, in Slaven Bilic, we have secured the services of an experienced coach who has recent experience of promotion to the Premier League."
Guoan are the eighth club of Bilic’s managerial career after also having spells with Hajduk Split, Lokomotiv Moscow, Besiktas, West Ham United and Al-Ittihad.
Bilic also managed the Croatia national team between 2006 and 2012.
