Mitchell, 22, had joined Annan Athletic on loan from the Ibrox side in 2013, playing 11 matches and scoring twice.
His Rangers contract was terminated by mutual consent in January, and he joined Annan on a permanent deal until the end of the season.
The Northern Irishman tasted success as a youth player with Manchester City prior to joining Rangers, helping City to victory in the Al Ain International Championship in 2010.
Southport boss Martin Foyle, who also signed former Wigan defender Johnny Lynch, told southportfc.net that the new signings were ‘tenacious and willing to learn’.
The Merseyside club finished 18th in the Conference Premier last season.