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:
1:10pm Monday 15th September 2014
BRIAN Howard has signed a short-term contract with Oxford United after a successful trial.
10:50am Monday 15th September 2014
OXFORD United could have a new face in the squad against Accrington Stanley tomorrow night as they close in on a signing.
9:30am Monday 15th September 2014
MICHAEL Appleton was critical of Oxford United’s senior players as their winless start to the league season stretched to seven games with a 1-1 draw at fellow strugglers Exeter City.
7:30am Monday 15th September 2014
SCORING for Oxford United was the realisation of a boyhood dream for Callum O’Dowda, writes DAVID PRITCHARD.
6:59pm Sunday 14th September 2014
Watch match highlights of Oxford United's visit to Exeter City yesterday.