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:
5:03pm Saturday 20th September 2014
OXFORD United produced an entertaining display but had to settle for a draw as they were unable to find a way past a dogged Stevenage.
5:49pm Saturday 20th September 2014
9:30am Saturday 20th September 2014
Jake Wright believes it will be key for Oxford United to avoid getting dragged into a physical contest if they are to build on a midweek win when Stevenage visit today.
8:00am Saturday 20th September 2014
Top scorer Danny Hylton and Brian Howard are expected to have recovered from midweek knocks to start for Oxford United today.
9:30am Friday 19th September 2014
TOM Newey hopes Oxford United’s supporters will embrace the side’s progressive style after seeing them make it work for the first time at the Kassam Stadium.