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:
11:07pm Tuesday 21st October 2014
10:00pm Tuesday 21st October 2014
DANNY Hylton scored twice in 109 seconds as Oxford United came from behind to claim their first away league win in an enthralling game at Sixfields.
3:51pm Tuesday 21st October 2014
MATT Bevans could miss the rest of the season after undergoing knee surgery yesterday.
9:00am Tuesday 21st October 2014
Michael Appleton has urged Oxford United to make the most of an opportunity this week to end their wait for an away win.
8:00am Tuesday 21st October 2014
Michael Collins says Oxford United’s thrashing on their last away trip will act as a powerful motivation to get a positive result at Sixfields tonight.