Monaghan, 26, returns to Cables having left last year to move to Australia, before returning recently and having a spell with Witton Albion.
Southworth has recently been with Irlam FC.
A club spokesperson said: “It has taken a lot of work from our management team to get his over the line but I’m sure you will all agree that it was well worth the wait.”
Meanwhile, the club has also promoted two players from its reserve team - Ethan Van-Aston and Matty Scoullar.
Scoullar recently had a spell at Skelmersdale, giving him a taste of first team football.
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