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:
12:34pm Tuesday 25th November 2014
JAMES Roberts could return to Oxford United action in three or four weeks after his hamstring injury was found to be less serious than initially feared.
8:00am Tuesday 25th November 2014
Michael Appleton is keen to loan out a couple of senior Oxford United players before the window closes on Thursday.
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.