The National League North side parted company with Jim Bentley in March following a difficult run of results.
Port went on to end the season in 18th place and have higher ambitions in 2025/26.
Danns, the former Crystal Palace, Macclesfield and Bury midfielder, joins after leaving Tranmere Rovers with former Southport player Mark Duffy arriving as his assistant manager.
The 42-year-old said: “I can’t wait and I’m really excited. I’m really thankful for the opportunity.
“My job is to make sure we have a squad ready for pre-season, when we get down to work.”
Southport confirmed in a club statement: “We are delighted to announce our new management team of Neil Danns as manager and Mark Duffy assistant manager.
“Neil joins the club after spending two years as Assistant Manager at Tranmere Rovers.
“Following a 20-year playing career, Neil made the transition into coaching and management, being appointed as player-manager by Macclesfield and leading them to promotion to the Northern Premier League as champions before being appointed as assistant manager at Tranmere Rovers in May 2023.
“Mark Duffy is no stranger to Haig Avenue where he made 103 appearances in total scoring 19 goals in all competitions.
“Mark was actually named as the head coach at Macclesfield following the departure of Neil Danns from Macc and after leaving The Silkmen he had a short spell as manager at Warrington Rylands.
“We extend a very warm welcome to Haig Avenue to Neil and Mark and hope they enjoy a successful time at the club.”