Lund Hansen has been at Rosenborg since 2002, but decided to leave the club at the end of this season.
He told RBK.no: “OB is a big club that has ambitions of being at the top of Danish football. They are at the top of the league at the moment.
“I want to try something new, after failing to make an impact at Rosenborg.”
Lund Hansen will face competition from former Manchester United keeper Roy Carroll at Odense.