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:
12:00pm Thursday 30th October 2014
OXFORD United's Tom Newey has agreed a loan move to Northampton Town until January.
9:40am Thursday 30th October 2014
ONE of Oxford United’s senior players is expected to finalise a move away from the club today.
9:30am Wednesday 29th October 2014
MICHAEL Appleton says fresh starts are needed for out-of-favour players at Oxford United – and admits it could mean they end up leaving permanently.
9:00am Tuesday 28th October 2014
Michael Appleton is expecting a tricky test when he returns to one of his former clubs with Oxford United in the FA Cup first round.
8:00am Tuesday 28th October 2014
Gary Rowett, who yesterday became Birmingham City’s new manager, was once on Oxford United’s radar, according to a statement issued by Burton Albion.