Edwards only took over at Vicarage Road at the end of last season, leaving Forest Green Rovers to replace Roy Hodgson following the Hornets' relegation from the Premier League.
Watford relieved Edwards and his assistant Richie Kyle of their duties on Monday and swiftly confirmed Bilic had taken the hot seat, signing an 18-month contract – subject to securing a work permit.
The former Croatia defender had been out of work since leaving Beijing Guoan in January but will be the Championship club's fifth boss in less than a year.
Watford FC confirms Slaven Bilić as its new Head Coach on an 18-month contract, subject to receiving the relevant work permit.— Watford Football Club (@WatfordFC) September 26, 2022
Bilic, who was promoted with West Brom in 2019-2020, takes over a side 10th in the table, just one point off the play-offs.
"As with all decisions taken by the board, I believe this change to be in the best interests of the club," said Watford 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."
Claudio Ranieri and Hodgson had spells in charge of Watford last season after Xisco Munoz was fired in October.