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:
9:00am Thursday 28th May 2015
OXFORD United’s ability to land their main targets this summer is down to selling players a vision for the future rather than offering the most money, according to chief executive Mark Ashton.
8:50am Thursday 28th May 2015
OXFORD United have announced big changes in their retail department, which will give them more control over their design of merchandise.
9:30am Wednesday 27th May 2015
RYAN Taylor is relishing the prospect of battling for a place in Oxford United’s striking quartet next season after completing his move yesterday.
5:30pm Tuesday 26th May 2015
RYAN Taylor has become Oxford United's third signing of the summer after agreeing a two-year deal with the club.
9:10am Tuesday 26th May 2015
Oxford United have been named as one of the favourites for the Sky Bet League Two title next season.