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:
8:00am Tuesday 28th April 2015
Johnny Mullins is set to miss Oxford United’s final game of the season with concussion sustained in Saturday’s 2-0 win against Cambridge United.
12:50pm Monday 27th April 2015
JOHNNY Mullins praised Oxford United’s medical staff for their swift action after being concussed following a horror fall against Cambridge United.
9:30am Monday 27th April 2015
DANNY Hylton was honoured to be voted player of the season by Oxford United’s supporters and capped it off with an excellent display in a 2-0 win against Cambridge United.
8:40am Monday 27th April 2015
MICHAEL Appleton felt Oxford United’s performance deserved more than their 2-0 win against Cambridge United, but was delighted to finish on a high in front of the home fans.
3:03pm Sunday 26th April 2015
WATCH the best moments as Oxford United signed off at the Kassam Stadium with a comfortable 2-0 win against Cambridge United.