The iconic striker, who is just one goal short of equalling the all-time goalscoring record, was offered a new contract after his previous deal expired at the end of the season.
But the 29-year-old has rejected the terms.
He told the club's official website: “I have absolutely loved my time at the club and would like to thank everyone for making my time there so special.
"The fans have been unbelievable and I can’t thank them enough for everything.
"The club has been a massive part of my life for the last six years and it’s sad to be leaving but now I am looking forward to the next stage of my career.”
Eastleigh, who last season won promotion into the Conference Premier, are managed by former U's player Richard Hill.
He was delighted to have secured Constable's services.
"I’ve spent the past two-and-a-half weeks speaking to James and telling him all about what we are striving to achieve here," Hill said.
"On the three occasions we’ve met, and during numerous telephone conversations, the subject of money has never been raised.
"In truth, James was keen to stay at Oxford and overhaul the club’s scoring record; a feat that after six years of committed service there he was desperate to achieve.
"He was initially holding out in the hope that Oxford would offer him fair terms to stay and do that.
"Oxford’s loss, though, is definitely our gain."
- You can leave your messages and tributes to Beano in the comments section below or email them to us and we shall pass them on to him.
Latest United news:
3:51pm Tuesday 21st October 2014
MATT Bevans could miss the rest of the season after undergoing knee surgery yesterday.
9:00am Tuesday 21st October 2014
Michael Appleton has urged Oxford United to make the most of an opportunity this week to end their wait for an away win.
8:00am Tuesday 21st October 2014
Michael Collins says Oxford United’s thrashing on their last away trip will act as a powerful motivation to get a positive result at Sixfields tonight.
10:42am Monday 20th October 2014
OXFORD United bounced back to form with a 2-0 win against Tranmere Rovers at the Kassam Stadium.
9:30am Monday 20th October 2014
ALFIE Potter hailed a “perfect day” as he came off the bench to score and give Oxford United a much-needed victory over Tranmere Rovers.