Barrow return to the Football League for the first time in 48 years when they were named champions of the National League after the season was curtailed by the coronavirus pandemic.
Evatt departed Barrow at the beginning of July after landing the job to take charge of League Two outfit Bolton Wanderers.
Barrow chairman Paul Hornby said, "As soon as we knew David was available and wanted the position we made him our number one target. He is an extremely talented coach and ticked all the boxes with the owners.
"His football philosophy and style of play is completely suited to how we are setup and he also knows a number of our players, which met our requirements for a seamless transition.
"After meeting David we knew he would be the man to take the club onto the next level."