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:
3:03pm Sunday 26th April 2015
WATCH the best moments as Oxford United signed off at the Kassam Stadium with a comfortable 2-0 win against Cambridge United.
5:53pm Saturday 25th April 2015
5:02pm Saturday 25th April 2015
GOALS from Kemar Roofe and Danny Hylton saw Oxford United win their final home game of the season at a canter against Cambridge United.
9:30am Saturday 25th April 2015
Michael Collins expects a reminder of Oxford United’s heavy defeat at Cambridge United earlier in the season will be pinned up in the changing room to act as motivation ahead of their rematch today.
9:00am Saturday 25th April 2015
A minute's silence will be held at Oxford United before kick-off this afternoon to commemorate the 30th anniversary of the Bradford City fire.