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:
6:40am Wednesday 1st October 2014
JAMES Roberts admitted it was extra sweet to score a winner for Oxford United against rivals Swindon Town, even if it came in a behind-closed-doors game.
3:26pm Tuesday 30th September 2014
JAMES Roberts came off the bench to score the winner as Oxford United came from two goals down to win 3-2 against Swindon Town at Roman Way.
9:00am Tuesday 30th September 2014
Oxford United’s position in the table is now a concern for head coach Michael Appleton, who has acknow-ledged it is taking longer than expected to improve results.
8:00am Tuesday 30th September 2014
A lacklustre Oxford United Women suffered a 5-0 thrashing at local rivals Reading, writes MATTHEW BRUCE.
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.