The 33-year-old took charge of the Sandgrounders in March after former manager Dino Maamria left the club for "family and travel reasons".
Southport have lost just once in seven games under player-manager Bishop to climb from 17th in the table to 15th.
"I've played a lot at this level so I know what it takes," he told the club website.
"I've really enjoyed every aspect of management so far. My target is to improve on this season and let's see where it takes us."
National League side Southport have appointed interim boss Andy Bishop as manager on a full-time basis.