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:
2:00pm Friday 19th December 2014
BRIAN Howard’s situation at Oxford United is unclear after head coach Michael Appleton admitted he did not know whether the midfielder would be offered an extension to his short-term contract.
12:00pm Friday 19th December 2014
JOSH Ashby is good enough to play in Oxford United’s side right now, but the teenager knows his time will come, according to head coach Michael Appleton.
9:40am Friday 19th December 2014
RONNIE Moore is braced for a tough first game in charge of Hartlepool United after comparing opponents Oxford United to Real Madrid.
9:30am Friday 19th December 2014
John Campbell admits it would be difficult to keep his kit on if he was able to make an impact on debut for Oxford United tomorrow.
Interactive match preview: Appleton and Hylton on goals; Moore likens United to Real Madrid; Howard's future; Ashby; club stalwart departs + video
9:34am Friday 19th December 2014
Get ready for kick-off with our interactive preview of Oxford United's trip to Hartlepool