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:
6:59pm Sunday 14th September 2014
Watch match highlights of Oxford United's visit to Exeter City yesterday.
4:58pm Saturday 13th September 2014
THE wait for a win goes on for Oxford United and Exeter City after the pair shared the points at St James Park.
5:48pm Saturday 13th September 2014
9:20am Saturday 13th September 2014
Danny Rose believes last weekend’s results will give Oxford United a psychological edge as they visit fellow winless side Exeter City this afternoon.
9:30am Friday 12th September 2014
OXFORD United are poised to launch an ambitious plan which chief executive Mark Ashton believes will eventually set the club apart from their rivals.