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:
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.
9:30am Friday 24th October 2014
James Roberts is in no mood to rest on his laurels as the young Oxford United striker looks to feature in a fourth successive game when they visit Carlisle United tomorrow.
9:20am Friday 24th October 2014
ALFIE Potter says the secret to his return to form has been learning to enjoy football again after a difficult spell.
9:10am Friday 24th October 2014
MICHAEL Collins has revealed Oxford United are using a reminder of their hammering at Cambridge United to get fired-up for games.