Holley and Johnson celebrate Magners League success in 2010
However, hopes that the Ospreys could move beyond the Heineken Cup quarter-finals were not realised in subsequent seasons.
The Swansea-based region did not reach the 2010-11 knock-out stages and a
36-5 defeat by Biarritz
in this season's final Pool Five clash ended their hopes, after they had also twice lost to Saracens and drawn at Treviso.
They currently lie second to Leinster in the RaboDirect Pro12 League (the successor to the Magners League) and maintain hopes of repeating their 2010 success.
Ospreys praised Holley's contribution over recent years, saying he can be "justifiably proud of all he has achieved".
But Cuddy added: "Sean is in agreement with us that in order to move forward professionally, he too is now in a position where he needs a new challenge.
"And by moving on with immediate effect, it allows both him and the Ospreys to draw a clear line under the past and move forward with a fresh impetus."
In a statement, 41-year-old Holley said: "It's going to be a very different way of life and a difficult one at first. I guess I've become part of the furniture.
"However that has also become part of the issue and I've done a lot of on field coaching as well as off-field work during this job. I have a young family to consider so it's time I took a bit of a break from it and recharge myself."
In December 2011, Johnson announced his intention not to look to renew his contract after accepting an offer to join the Scottish Rugby Union.
But his departure has now been brought forward following the announcement of Holley's departure.
"After extensive discussions, Scott has offered to step down from his post now rather than at the end of the season, and we have agreed to release him from the remaining terms of his contract," said Ospreys chief operating officer Andrew Hore.
"It was a gesture that he has made for the good of the Ospreys business and is typical of the way he has continuously put the region first during his three years as director of coaching."
Tandy's first game in charge with be the Pro12 match with Aironi at the Liberty Stadium on Friday.
Flanker and Welsh Rugby Union/Ospreys regional community manager Ben Rose will take at Bridgend until the end of the season.
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