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:
10:42am Monday 20th October 2014
OXFORD United bounced back to form with a 2-0 win against Tranmere Rovers at the Kassam Stadium.
9:30am Monday 20th October 2014
ALFIE Potter hailed a “perfect day” as he came off the bench to score and give Oxford United a much-needed victory over Tranmere Rovers.
8:20am Monday 20th October 2014
JAKE Wright praised the performance of debutant Tareiq Holmes-Dennis in Oxford United’s win over Tranmere Rovers.
6:30am Monday 20th October 2014
MICHAEL Appleton said his selection on Saturday should alert Oxford United’s players that they have to perform or face being dropped.
5:56pm Saturday 18th October 2014