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:
9:30am Friday 27th March 2015
KYLE Vassell is hoping to end the season with a bang – by scoring goals and firing Oxford United to safety.
9:00am Friday 27th March 2015
MICHAEL Appleton knows it is the issue that has dogged Oxford United all season.
8:30am Friday 27th March 2015
KEITH Curle says he plans on making life difficult for Oxford United at the Kassam Stadium tomorrow.
7:20am Friday 27th March 2015
INCREDIBLY, Michael Appleton is now exactly halfway on the list of long-serving Football League managers.
6:20am Friday 27th March 2015
OXFORD United fans are being encouraged to try something a little different with the launch of a footgolf course.