The 27-year-old had originally joined the Eagles on a season-long basis back in August.
However, the winger has now agreed a contract at Selhurst Park that will expire in the summer of 2018, with the Saints having accepted an undisclosed offer.
"It's great to sign a permanent deal, it's something I dreamt about when I was a kid so I'm pleased to get it done. I was here when I was eight when the likes of Dean Gordon and Chris Armstrong were here so that makes its special," he told the club's official website.
"The massive factor in this was the chairman and the manager, the gaffer has shown great faith in me since he's been here and that's been unbelievable for me. It's a boost for me mentally - I thought it might happen at the end of the season but it's come quicker and obviously that's good for both me and the football club."
Puncheon has scored three goals during his 20 Premier League outings this term.