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:
5:46pm Saturday 30th August 2014
Oxford Utd 3 (Jakubiak 3, Hylton 55 & pen 61) Dagenham & Redbridge 3 (Hemmings 7, Cureton 46, Ogogo 71)
5:00pm Saturday 30th August 2014
A BREATHLESS game saw Oxford United get off the mark in Sky Bet League Two as they shared six goals with visitors Dagenham & Redbridge.
9:30am Saturday 30th August 2014
Johnny Mullins is confident Oxford United’s midweek cup exertions will be a help rather than a hindrance in the search for their first points of the season today.
8:30am Saturday 30th August 2014
Michael Appleton has warned Oxford United to be on their guard against veteran goalscorer Jamie Cureton this afternoon.
6:12pm Friday 29th August 2014
OXFORD United have loaned out Aidan Hawtin and Josh Shama to Banbury United plus Matt Bevans to Farnborough.