The club announced the arrival of Bilic minutes after reporting that Edwards had been fired after just 11 games in charge in all competitions.
Watford, relegated from the Premier League last season, are 10th in the Championship, the second tier of the English game, with three wins from 10 league games.
"As with all decisions taken by the board, I believe this change to be in the best interests of the club," said Hornets owner Gino Pozzo.
"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."
Former Croatia international and national team coach Bilic guided West Brom to promotion in the 2019/20 season and has since managed in China.
