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:
7:50am Wednesday 28th January 2015
REPORTS suggesting Tyrone Barnett had rejected personal terms at Oxford United are wide of the mark, says chief executive Mark Ashton.
3:21pm Tuesday 27th January 2015
TOM Newey has signed a contract at Northampton Town until the end of the season, 24 hours after leaving Oxford United.
11:10am Tuesday 27th January 2015
JOE Skarz admitted it took plenty of thought to drop two divisions and join Oxford United, but was swayed by the club’s potential.
11:00am Tuesday 27th January 2015
OXFORD United’s bid for Tyrone Barnett shows their commitment to strengthening the squad as the January transfer window enters its final week, according to chief executive Mark Ashton.
5:40pm Monday 26th January 2015
TOM Newey has agreed a settlement to leave Oxford United early by mutual consent.