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:
12:30pm Thursday 29th January 2015
OXFORD United have signed Richard Brindley on an initial one-month loan deal from Rotherham United.
10:44am Thursday 29th January 2015
JOHN Campbell's future at Oxford United is up in the air as discussions with Jarrow Roofing continue.
9:00am Thursday 29th January 2015
ALFIE Potter says he will always have great memories from his time at Oxford United.
9:10am 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.