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:
2:43pm Tuesday 23rd September 2014
ANDY Whing and Ryan Clarke played their first games of the season as Oxford United's development side came from behind to win 2-1 against Southend United.
9:30am Tuesday 23rd September 2014
OXFORD United will get a double fitness boost today as Ryan Clarke and Andy Whing make their re-turn to playing after surgery this summer.
8:20am Tuesday 23rd September 2014
OXFORD United came from behind to secure a 2-2 draw at home to Durham, extending their unbeaten run to three games in the process, writes MATTHEW BRUCE.
12:50pm Monday 22nd September 2014
OXFORD United extended their unbeaten run to five games with a goalless draw at home to Stevenage.
9:30am Monday 22nd September 2014
MICHAEL Appleton rued some over-elaborate finishing, but was heartened by Oxford United’s commanding display against Stevenage.