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:
12:30pm Thursday 20th November 2014
OXFORD United have completed the signing of Chey Dunkley from Kidderminster Harriers.
9:30am Wednesday 19th November 2014
OXFORD United set up a glamour trip to Manchester City in the FA Youth Cup as they saw off rivals Swindon Town 3-2 at the Kassam Stadium.
9:00am Wednesday 19th November 2014
CHEY Dunkley is expected to complete his move to Oxford United today after international duty delayed the transfer from Kidderminster Harriers.
9:25pm Tuesday 18th November 2014
JORDAN Graham scored twice but Oxford United had to survive a late scare on the way to knocking rivals Swindon Town out of the FA Youth Cup at the Kassam Stadium.
2:43pm Tuesday 18th November 2014
JOSH Ashby and Callum O'Dowda were on target as Oxford United went down 3-2 to Bournemouth in a development game at Roman Way.