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:
9:30am Thursday 18th September 2014
CALLUM O’Dowda has all the attributes to progress and play at a higher level, according to Oxford United teammate Johnny Mullins.
5:17pm Wednesday 17th September 2014
OXFORD United claimed their first Sky Bet League Two victory of the season with a 3-1 success at home to Accrington Stanley on Tuesday night.
9:30am Wednesday 17th September 2014
MICHAEL Appleton admitted a weight had been lifted off Oxford United’s shoulders as they avoided an unwanted club record by beating Accrington Stanley 3-1 to claim their first league victory of the season.
11:04pm Tuesday 16th September 2014
9:44pm Tuesday 16th September 2014
THERE was relief all round as Oxford United ended their long wait for a league win at the expense of ten-man Accrington Stanley at the Kassam Stadium.