Full back joins League One rivals.
Ryan, who joined the U's after trialling during pre-season in the summer of 2013, has opted to go to the Sussex side on a two year contract.
He had been offered a new deal by the U's but will now come up against them in the 2014/15 season after joining John Gregory's side.
U's boss Joe Dunne wanted him to remain at the Weston Homes Community Stadium but accepted that the left back may seek a future elsewhere.
Dunne said: "We would have liked Ryan to stay but fully understand that he wanted to find the best deal for himself and his family."
"He is moving onto the next chapter in his career, we wish him well in that, and now he's made this decision, we'll move onto the list of potential replacements in that position."
Dickson's switch to the Checkatrade.com Stadium means that only Mark Cousins and David Wright's futures are left to be sorted from last season's squad.