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 Wednesday 6th May 2015
OXFORD United have taken the bold step of reducing prices for season tickets across the board when they go on sale this morning.
9:20am Wednesday 6th May 2015
AWAY supporters at the Kassam Stadium will not be moved next season after Oxford United considered a variety of alternatives.
9:00am Tuesday 5th May 2015
Michael Appleton is confident Oxford United’s strong form at the end of the season can be translated into prolonged success across the whole of the next campaign.
12:20pm Monday 4th May 2015
Michael Appleton wished the end of the season was still a month away after Oxford United continued their strong form with a 1-0 win at Newport County.
12:10pm Monday 4th May 2015
Sam Humphreys was thrilled to finally make his senior debut for Oxford United, 12 years after joining the club.