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:
3:40pm Wednesday 27th August 2014
ULTIMATELY it was a heartbreaker for Oxford United, but here are match highlights from the U's Capital One Cup clash against Premier League West Bromwich Albion last night
9:30am Wednesday 27th August 2014
MICHAEL Appleton was hugely proud by the way Oxford United stood up to West Bromwich Albion as a dramatic night saw the underdogs knocked out after a penalty shoot-out.
1:42am Wednesday 27th August 2014
10:56pm Tuesday 26th August 2014
OXFORD United put in a magnificent effort as they took West Bromwich Albion all the way to a penalty shoot-out at the Hawthorns.
9:30am Tuesday 26th August 2014
WILL Hoskins is champing at the bit to get started at Oxford United and the striker is hopeful he can make his debut at West Bromwich Albion tonight (8).