The newly-relegated League Two side have clinched the former Wales international's signature after he turned down the chance to manage a Premier League club.
"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."
The 41-year-old recently left his role at Exeter City, where he helped guide the club to successive promotions from the Conference to League One.