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:
5:55pm Saturday 24th January 2015
5:01pm Saturday 24th January 2015
JAMES Roberts struck a stoppage-time equaliser as Oxford United stopped the rot with a draw at home to Exeter City.
2:50pm Saturday 24th January 2015
OXFORD United have made their first addition of the January transfer window by signing Joe Skarz.
9:00am Saturday 24th January 2015
Johnny Mullins says Oxford United’s squad have the quality to get themselves out of trouble even without help from new signings.
8:00am Saturday 24th January 2015
THE KASSAM Stadium will echo to a minute’s applause this afternoon to mark the death of a lifelong U’s fan.