The Republic of Ireland international has agreed to join the League Two outfit from Championship side Yeovil Town on a two-and-a-half year deal
The 23-year-old striker joins the League Two leaders from Yeovil Town on a two-and-a-half year deal.
Madden, who was the top goalscorer in League One last season during Yeovil's promotion charge, opted to drop divisions in search of regular football.
This season, the former Bohemians striker has failed to score a competitive goal, making just nine league appearances for the Glovers.
"I am as disappointed as anyone else that things haven't worked out this season for Paddy for whatever reason," Yeovil boss Gary Johnson told the club's official website. "These things happen in football and we all move on.
"I would like to thank Paddy for his service to our football club and we all wish him well for the future."
Meanwhile, Shane Duffy says that he is "loving" his time at Yeovil Town after agreeing to extend his loan at the club until the end of the season.
The Republic of Ireland Under-21 captain has been ever-present for the club since joining on loan at the end of September and has revealed that he is enjoying his time at Huish Park.
"I'm loving it," Duffy told the club's official website. "It's just so important for me to be out there every week learning. I'm learning so much every game against different opponents and I'm thriving on it.
"[Everton] are watching every game. They're happy with me. They were happy for me to stay here because I'm learning; we're defending most games, so it wouldn't do any harm to stay here."