Bostock announced the departures Tuesday in a letter to shareholders, describing the moves as part of Yahoo's turnaround efforts.
"The board has concluded that in order to accelerate the Company's transformation, the combination of a new Chief Executive Officer with an enhanced team of independent directors would provide Yahoo with the expertise and perspectives necessary to drive innovation and growth going forward," Bostock said in the letter.
"Therefore, Mr. Joshi, Mr. Kern, Mr. Wilson and I have volunteered not to stand for re-election at the next shareholders' meeting."
Yahoo's new CEO, hired last month, is Scott Thompson, the former president of EBay's PayPal unit. The board shake-up will leave the company with no board members who have joined earlier than 2010, Bostock said.
"We believe that this reconfigured board, with a fresh set of perspectives and diverse set of skills, will enable the company to move forward even more aggressively," he said.
Along with the departures, Bostock announced that two new directors would join Yahoo -- Alfred Amoroso and Maynard Webb Jr. Bostock's letter described them as highly qualified.
"Amoroso served as President and CEO of Rovi Corporation until December 2011 and, among other positions, had previously served as the President, CEO and Vice Chairman of META Group, Inc., the President and CEO of CrossWorlds Software, Inc. and as a member of the world-wide management committee of IBM Corporation," Bostock said.
"Webb, the Chairman of LiveOps, Inc., served as that company's CEO until July 2011. Prior to that, Mr. Webb was Chief Operating Officer of eBay and Senior Vice President and Chief Information Officer for Gateway, Inc., in addition to management, leadership and board positions at several other companies spanning his 30-year career," he said.
The board is looking to add more directors as well, with that search led by board member Patti Hart, the CEO of International Game Technology Inc., the letter said. Hart is also the chair of Yahoo's nominating and corporate governance committee.
The move follows the resignation of company founder Jerry Yang, who left Yahoo's board in mid-January.
The company's ongoing review of how to reshape itself has been underway since Yahoo fired its previous CEO, Carol Bartz, in September. Bartz had served as Yahoo's chief executive since January 2009, when she was hired with the hope of reversing the company's declining revenue.
As a part of its self-review process, Yahoo is examining what assets and operations to keep and what to shed, including a critical look at its investments and businesses in China and Japan.
"As part of this review, we have pursued a wide range of discussions with potential partners," Bostock said in the letter. "We have engaged with potential investors and reviewed proposals concerning an equity investment in the company, although at this time there have not been any proposals which have been deemed by the committee to be attractive to our shareholders.
"We are also in active discussions with our partners in Asia regarding the possibility of restructuring our holdings in Alibaba Group and Yahoo! Japan. The complexity and unique nature of these transactions is significant. While we continue to devote significant resources to these discussions, we are not in a position at this time to provide further detail or to provide assurance that any transaction will be achieved."
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