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:
12:50pm Monday 22nd September 2014
OXFORD United extended their unbeaten run to five games with a goalless draw at home to Stevenage.
9:30am Monday 22nd September 2014
MICHAEL Appleton rued some over-elaborate finishing, but was heartened by Oxford United’s commanding display against Stevenage.
7:00am Monday 22nd September 2014
JOE Riley said no-one at Oxford United would be critical of Danny Hylton after the top scorer wasted several good chances in the goalless draw with Stevenage.
5:03pm Saturday 20th September 2014
OXFORD United produced an entertaining display but had to settle for a draw as they were unable to find a way past a dogged Stevenage.
5:49pm Saturday 20th September 2014