Edwards leaves his role as assistant manager to Paul Tisdale at Exeter City to take up the reins at Prenton Park, and will look to revive the fortunes of the club after their relegation from League One last season.
The 41-year-old helped guide Exeter from non-league football up to play-off contenders in the third tier of English football and hopes to have a similar effect on Tranmere.
"I would like to thank everyone at the club for this fantastic opportunity," Edwards told the club's official website. "I've worked hard for this chance and feel I've been ready to manage for some time.
"I've ready to put into practice the skills I've learned from 25 years in the game that has seen me work with, and learn from, some superb managers and excellent players.
"I believe I can develop a team at Tranmere Rovers the whole club, and the whole of Wirral can be proud of.
"My aim is to make sure we are challenging at the top end of the table, as well as setting up a structure to produce more home grown players.
"I'm looking to move the club forward with an attacking brand of high-energy football and I can't wait to get started."
Edwards' predecessor Ronnie Moore was sacked in April after admitting a Football Association charge of misconduct in relation to betting.
