The 30-year-old, who was released by AFC Wimbledon earlier this month, signed two days after Constable made the switch to the Skrill South champions.
It brings the pair together for a second time, after they combined to good effect in the United squad which won promotion back to the Football League via the play-offs in 2010.
The Hampshire club are managed by former U’s midfielder Richard Hill, who felt a second big signing in succession showed they meant business next season.
He said: “Like James Constable, Jack is an extremely ambitious lad and, to come and play in the Conference, he needed to be convinced that we’re not going into this league just to tread water.”
Latest United news:
11:00am Monday 24th November 2014
OXFORD United were unable to break down a well-organised AFC Wimbledon side during their goalless draw at the Kassam Stadium on Saturday.
10:43am Monday 24th November 2014
Explore your way around our interactive back page - eight links for your best local sports coverage, including our Oxford United match picture gallery. And there's video highlights from U's clash with AFC Wimbledon as well..
9:30am Monday 24th November 2014
ALFIE Potter admitted it was a big blow for everyone at Oxford United to see James Roberts limp off on Saturday.
8:40am Monday 24th November 2014
MICHAEL Appleton refused to be too downbeat and instead praised the way Oxford United stuck to the game plan as they drew a blank against AFC Wimbledon.
7:40am Monday 24th November 2014
ANDY Whing relished playing his part in restricting Adebayo Akinfenwa’s impact as Oxford United shared a goalless draw with AFC Wimbledon.