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:
12:00pm Friday 19th December 2014
JOSH Ashby is good enough to play in Oxford United’s side right now, but the teenager knows his time will come, according to head coach Michael Appleton.
9:40am Friday 19th December 2014
RONNIE Moore is braced for a tough first game in charge of Hartlepool United after comparing opponents Oxford United to Real Madrid.
9:30am Friday 19th December 2014
John Campbell admits it would be difficult to keep his kit on if he was able to make an impact on debut for Oxford United tomorrow.
Interactive match preview: Appleton and Hylton on goals; Moore likens United to Real Madrid; Howard's future; Ashby; club stalwart departs + video
9:34am Friday 19th December 2014
Get ready for kick-off with our interactive preview of Oxford United's trip to Hartlepool
9:10am Friday 19th December 2014
THERE were times earlier this season when it felt like Danny Hylton was scoring in every game, but Oxford United’s top scorer is not getting weighed down by a sudden barren run in front of goal.