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:
9:30am Tuesday 21st April 2015
Michael Appleton has promised he will look players in the eye and tell them straight if they are not in his plans for Oxford United next season.
12:10pm Monday 20th April 2015
AN emotional Aidan Hawtin was overjoyed to make his professional debut for Oxford United, coming off the bench late on against Tranmere Rovers.
9:30am Monday 20th April 2015
Kemar Roofe insists he does not know where his future lies after netting his second double in a fortnight to help Oxford United to a 3-0 win at Tranmere Rovers on Saturday.
8:40am Monday 20th April 2015
THE quality of Oxford United’s first two goals had head coach Michael Appleton purring as his side thrashed Tranmere Rovers 3-0 at Prenton Park, writes DAVID PRITCHARD.
12:18pm Sunday 19th April 2015
WATCH the key moments from Oxford United's 3-0 win at Tranmere Rovers yesterday.