The 56-year-old was sacked by Chester in April after a run of just one win in 10 put the club in a relegation fight.
Southport relieved Andy Bishop of his duties on Saturday with the side lying second from bottom in the table.
Ex-Kidderminster boss Burr takes over a side that has picked up four points from their first eight league matches of the season, suffering six defeats.
National League side Southport have named former Chester boss Steve Burr as their new manager.