During the recruitment process, assistant coach Sean Holley and forwards coach Jonathan Humphreys will continue under Hore's guidance, but attention is likely to focus on the position of Director of Rugby Kevin Hopkins.
"Lyn has done an outstanding job in his time as Ospreys coach and, without doubt, has been the most successful coach in Wales since the onset of regional rugby," said Ospreys managing director Roger Blyth.
"He successfully led us through our challenging formative seasons, combining the rugby playing cultures of Neath and Swansea into a new dynamic.
"Having achieved so much, we whole-heartedly understand Lyn's desire to leave on a high and seek a new challenge in the next phase of, what I have no doubt, will remain an outstanding career coaching rugby.
"Our challenge is now to recruit a coach of worldwide calibre, capable of picking up the reigns from Lyn to drive the region forward and accelerate our development.
I feel it's now time to get my teeth into a new challenge
"We want the right man for the job and we are prepared to look hard and fight hard to get him."
Jones' squad provided the vast majority of Wales' 2008 Grand Slam side, but their defence of the Magners League ended in a woeful seventh-placed finish and the Heineken exit rocked the region.
"The last 10 years have been a tremendous time for me personally and professionally, with Neath RFC and the Ospreys," said Jones.
"The region now stands as one of the leading sides in European rugby and that is something that I know everybody involved at the Ospreys is proud of.
"I feel it's now time to get my teeth into a new challenge and that it is the best time for a new hand to come in and move the Ospreys to its next level of development."
Hore, who arrived at the Ospreys in March, has spent the last two months carrying out a head-to-toe review of the region.
He said after last month's impressive 23-6 EDF Energy Cup final win over Leicester that the result would have no bearing on his findings.
"One-off wins are not how we measure things, that's not what we're about," Hore told BBC Sport Wales at the time.
"We're assessing the whole region and individuals in it, and we're doing it in a measured and calculated way."
Jones is the second Welsh regional coach to depart after the end of the 2007/8 season, Phil Davies having left Llanelli Scarlets to be replaced by Nigel Davies.
Former Wales back-rower Emyr Lewis says that Jones' departure was to be expected.
"With the Ospreys' playing squad and the people they have behind the scenes they haven't had the results or the performances," Lewis told BBC Radio Wales.
"They got to the quarter-final of the Heineken Cup, but lost to a poor Saracens side.
"That should never have happened to a squad of their calibre. Lyn did not get the best out of his players."
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