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:
1:55pm Saturday 25th October 2014
All the news from Oxford United's visit to Carlisle United in Sky Bet League Two.
9:30am Saturday 25th October 2014
Danny Rose is targeting a move into mid-table today as Oxford United visit Carlisle United in search of a third win in eight days.
9:00am Saturday 25th October 2014
Michael Appleton is confident a sickness bug which has affected the Oxford United squad will not have an impact on selection against Carlisle United today.
11:30am Friday 24th October 2014
THE presence of Andy Whing back in the Oxford United side has prompted other players to raise their game, according to Michael Collins.
11:20am Friday 24th October 2014
KEITH Curle has demanded a strong start from Carlisle United when they host Oxford United at Brunton Park tomorrow.