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:
9:30am Monday 25th May 2015
LIAM Sercombe is aiming to help solve Oxford United’s search for goals from midfield next season.
6:00am Monday 25th May 2015
SWINDON Town and Wycombe Wanderers suffered play-off agony over the weekend.
9:30am Friday 22nd May 2015
Ryan Taylor remains firmly on Oxford United’s radar despite the signing of Kemar Roofe, according to head coach Michael Appleton.
9:30am Wednesday 20th May 2015
RYAN Clarke admits he would listen if the right opportunity came up this summer after being told he would not be certain of being Oxford United’s No 1 goalkeeper next season.
9:00am Tuesday 19th May 2015
Ryan Clarke has been told he will not be guaranteed to be Oxford United’s No 1 goalkeeper next season as head coach Michael Appleton keeps his options open.