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:
10:30am Monday 29th September 2014
MICHAEL Appleton admitted Oxford United were second best where it really mattered as they lost 2-0 at Luton Town.
10:24am Monday 29th September 2014
OXFORD United slipped back into the bottom two in Sky Bet League Two as they lost 2-0 at Luton Town.
8:10am Monday 29th September 2014
A RUEFUL Tyrone Barnett held his hands up for a missed header which turned out to be the key moment in Oxford United’s defeat.
7:30am Monday 29th September 2014
JOHNNY Mullins was disappointed Oxford United failed to heed the warnings about Luton Town’s fast start as they fell behind in just over a minute, writes DAVID PRITCHARD.
5:05pm Saturday 27th September 2014
OXFORD United's five-game unbeaten run came to a shuddering halt as they crashed to defeat at Luton Town.