The 38–year-old guided Barrow to the Vanarama National League title this season and back into the EFL for the first time since 1972.
Evatt arrived at The Progression Solicitors Stadium in 2018, finishing tenth with the Cumbrian side in his first season in charge.
They were crowned champions in June after the season was curtailed because of the COVID-19 pandemic.
Speaking to the club's website, chairman Paul Hornby said: "It’s always disappointing when someone decides to move on especially when they’ve had such a positive impact.
"Ian did a wonderful job over the time he was here and he leaves us with a blueprint and identity of how we want our team to play and a great group of players.
"We shouldn’t let his departure distract from a fantastic season and the massive opportunity promotion creates for this club going forward".