The 21-year-old has penned a two year deal at the club, while Hatters duo Dan Walker and Godfrey Poku have moved to Haig Avenue on loan until the end of December.
Kissock, who starred as Luton were beaten 2-1 by the Sandgrounders last season in Richard Money’s last game in charge, is a former England U16 and U18 international and current England C international.
He started his career at Everton, before spells at Gretna and Hamilton Academical and then dropped down to the Cheshire County League where he was spotted by Port boss Liam Watson.
Kissock scored for Southport in their opening day draw with Lincoln City and had a hand in the goal at Kenilworth Road last weekend when Luton ran out 5-1 winners.
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Hatters boss Gary Brabin told the club website: “I’m delighted to welcome John Paul to the Club. He’s a wonderful player, a crowd pleaser, who works hard and has terrific ability.
“He has enormous potential and we hope he will achieve big things at this football club. We’ve known about him for a while and only last week he showed what he’s capable of, when playing against us.
“John Paul can play anywhere in midfield or attack or the wing and has masses of energy, has fantastic touch and technique and, as well as from scoring goals, he can bring people into play.
“He’s going to be a massive player for us and I’m looking forward to working with him.”