The Irish forward, who scored 23 goals for the Glovers last campaign, has found first-team opportunities hard to come by in the Championship.
Madden, who joins the Iron for an undisclosed fee, told the club's official website: "I'm relishing the chance to play for Scunthorpe and to help them do well.
"I have had the feeling of promotion last season with Yeovil and I am hungry for more promotion so I am excited by this new challenge.
"Things were not working out at Yeovil Town so when I got told the chairman and gaffer here were on to me I was interested.
"Scunthorpe are a very ambitious club and I want to be part of that.
"The chairman has told me his plans for this club for the next couple of years and I bought into them straight away.
"It is very ambitious and hopefully I can help this club achieve promotion."