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:
9:20am Friday 24th October 2014
ALFIE Potter says the secret to his return to form has been learning to enjoy football again after a difficult spell.
9:10am Friday 24th October 2014
MICHAEL Collins has revealed Oxford United are using a reminder of their hammering at Cambridge United to get fired-up for games.
9:00am Friday 24th October 2014
WILL Hoskins continues to be well ahead of schedule in his recovery from a groin injury.
8:20am Friday 24th October 2014
OXFORD United’s next home game has been designated as Yellow Army Day by the club’s supporters’ group.
7:00am Friday 24th October 2014
STORIES from games at Oxford United’s former home are being collated for a new book, Up The Manor.