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:
11:20am Tuesday 31st March 2015
MAX Crocombe has been named on the bench for New Zealand's international friendly against the Korea Republic in Seoul today.
9:00am Tuesday 31st March 2015
Patrick Hoban thanked boss Michael Appleton and his Oxford United teammates for keeping faith in him after the longest scoring drought of his career came to an end.
8:00am Tuesday 31st March 2015
North Leigh manager Mark Gee will have just 12 players to choose from for tonight’s Oxfordshire Senior Cup semi-final against Oxford United at Banbury’s Spencer Stadium (7.45).
12:20pm Monday 30th March 2015
Michael Appleton thanked Oxford United’s supporters for the role they played in a critically-important 2-1 victory against Carlisle United.
12:10pm Monday 30th March 2015
WATCH the key moments from Oxford United's 2-1 victory against Carlisle United at the Kassam Stadium.