The Irishman, 26, only had six months remaining on his contract at Plainmoor and has opted to link up with play-off finalists Town on a two-year deal.
Having enjoyed previous spells with Blackpool and Scunthorpe, Morris joined the Gulls two years ago but missed most of last season with an Achilles injury.
"It's a fantastic move for him," Torquay manager Alan Knill told the club's official website. "He had a six-month contract with us but he phoned to say he'd been offered two years at Northampton.
"I think he'd already made up his mind and it's good news for him because having that security is very important."
And Cobblers boss Aidy Boothroyd is equally delighted to land a player who he feels will prove to be a positive addition to his promotion-chasing side.
"Ian is a very good player and I have followed his career closely," he said.
"He has always impressed me when I have seen him and I am pleased we have been able to bring him to the club. He can play in a number of positions and he has the experience of having played more than 200 games despite only being in his mid-20s.
"He is a winner, he has already won three promotions in his career and he has experience of playing in the Championship, League One and League Two. He is another player who will be a good addition to the squad and I am delighted we have got him."