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:
8:00am Friday 19th December 2014
ABOUT 150 supporters have taken advantage of Oxford United’s offer of free transport to tomorrow’s game at Hartlepool United.
7:00am Friday 19th December 2014
OXFORD United’s longest-serving member of staff has left the club following a restructure of the business.
9:08pm Thursday 18th December 2014
OXFORD United pushed Manchester City all the way as they were edged out of the FA Youth Cup 2-0 in the third round.
9:30am Thursday 18th December 2014
OXFORD United’s rising stars will get a taste of the big time tonight as they attempt a giant-killing against Manchester City in the FA Youth Cup (7).
6:30pm Wednesday 17th December 2014
JAMES Roberts edged closer to a first-team return for Oxford United after playing in a 2-0 win for the development side at Bournemouth.