Former Bury, Blackpool and Stockport striker Preece, 49, is the third manager at the Sandgrounders this season after Burr and Andy Bishop.
Director of football Liam Watson took temporary charge after Burr's four-month stint, as Southport sit a point above the relegation places.
"I am really looking forward to the challenge," said Preece.
"I've been in this situation before, taking over a club, and I expect to succeed. It is a big job."
He has previously been in charge of Bury, Worcester and Northwich, and spent four years as director of football at Welsh Premier League side Airbus UK Broughton, where they played in the qualifying rounds for the Europa League.
National League strugglers Southport have appointed Andy Preece as their new manager, replacing Steve Burr.