The 25-year-old rejected a better deal to stay at Sixfields in favour of a move to Cambridge United, who won promotion to the third tier last season.
Town boss Jon Brady was keen to keep hold of the central defender, who impressed last season after signing a short-term deal in December, but weeks of negotiations failed to find a breakthrough.
"I had a few offers but I spoke with the manager at Cambridge a while ago and I really liked what he had to say and what his plans are going forward and also the way he wants to play football," said Jones.
"The main thing was obviously to play League One football again, but the manager really impressed me as well and that made my mind up.
"Most of my minutes have been at this level but now I want to get a full season under my belt and do as well as I can at this club."
Cambridge will be playing third-tier football for the first time in 20 years next season.
"It feels really good to be here," Jones added. "The club did very well last season, winning promotion to League One, and I can't wait to get going.
"I like to see myself as a leader, I want to win and I'm quite composed on the ball."