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:
12:09pm Sunday 3rd May 2015
WATCH Kemar Roofe's wonder goal as Oxford United finished the season with a 1-0 win at Newport County.
5:54pm Saturday 2nd May 2015
5:02pm Saturday 2nd May 2015
A STUNNING strike from Kemar Roofe ensured Oxford United finished the season on a high with a hard-fought win at ten-man Newport County.
9:30am Saturday 2nd May 2015
Alex MacDonald hopes Oxford United can pick up where they left off last week to finish the season in style at Newport County today.
8:30am Saturday 2nd May 2015
Chey Dunkley and Andy Whing are set to continue their experimental defensive partnership for Oxford United today.