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:
7:00am Monday 22nd September 2014
JOE Riley said no-one at Oxford United would be critical of Danny Hylton after the top scorer wasted several good chances in the goalless draw with Stevenage.
5:03pm Saturday 20th September 2014
OXFORD United produced an entertaining display but had to settle for a draw as they were unable to find a way past a dogged Stevenage.
5:49pm Saturday 20th September 2014
9:30am Saturday 20th September 2014
Jake Wright believes it will be key for Oxford United to avoid getting dragged into a physical contest if they are to build on a midweek win when Stevenage visit today.
8:00am Saturday 20th September 2014
Top scorer Danny Hylton and Brian Howard are expected to have recovered from midweek knocks to start for Oxford United today.