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:
5:50pm Saturday 22nd November 2014
4:56pm Saturday 22nd November 2014
OXFORD United's winning run against AFC Wimbledon came to an end as they played out a goalless draw at the Kassam Stadium.
1:02pm Saturday 22nd November 2014
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9:30am Saturday 22nd November 2014
Michael Appleton says Oxford United will need to be intelligent if they are to keep heavyweight striker Adebayo Akinfenwa quiet for AFC Wimbledon today.
2:00pm Friday 21st November 2014
MICHAEL Appleton is keen to explore further the talent pool on offer in Ireland following the signing of Patrick Hoban.