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:
9:00am Tuesday 2nd September 2014
Michael Appleton is determined to do his shopping earlier next summer after Oxford United were unable to land their top target before the transfer window shut last night.
8:00am Tuesday 2nd September 2014
Michael Raynes is among the Oxford United players hoping to benefit from a run-out in the Johnstone’s Paint Trophy at Cheltenham Town tonight (7.45).
12:10pm Monday 1st September 2014
MICHAEL Appleton says Oxford United are in advanced talks with their top target, but there are no guarantees a deal will be finalised before the deadline closes tonight.
11:24am Monday 1st September 2014
Oxford United got off the mark in Sky Bet League Two with a 3-3 draw at home to Dagenham & Redbridge on Saturday.
9:30am Monday 1st September 2014
MICHAEL Appleton admitted he had never seen a game so wide open as Oxford United got off the mark with a topsy-turvy 3-3 draw at home to Dagenham & Redbridge.