Edwards, who began as a youth coach at Wolves before going on to manage AFC Telford United and Forest Green Rovers, where he won the League Two title last year, was appointed in the summer.
But with Watford, who were relegated last season currently tenth in the table, the club relieved Edwards of his duties and replaced him with former Baggies boss Bilic.
The Croatian took over at Albion in summer 2019 and led them to promotion back to the Premier League - before being sacked in December 2020.
He spent a year in charge at Beijing Guoan in China but left the role in January 2022.
He now takes over at Vicarage Road subject to receiving a work permit and is Watford's fifth manager in just the last 12 months.
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,” says Hornets’ owner Gino Pozzo of the move.
“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 Bilić, we have secured the services of an experienced coach who has recent experience of promotion to the Premier League.”
After taking the club Bilic now becomes the club's 21st manager in the last 12 years.