Bostock, in a letter to shareholders, also said Yahoo! was in "active discussions" with its partners in Asia on restructuring its holdings in the Alibaba Group and Yahoo! Japan.
Bostock said he had decided not to stand for re-election at Yahoo!'s next shareholders meeting, along with board members Vyomesh Joshi, Arthur Kern and Gary Wilson.
He said the board elected two independent directors Tuesday: Alfred Amoroso, former president and chief executive of Rovi Corp., and Maynard Webb, a former chief operating officer at eBay.
Bostock said a strategic review of Yahoo! has made "significant progress" and has included "a wide range of discussions with potential partners.
"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," he said.
"We are also in active discussions with our partners in Asia regarding the possibility of restructuring our holdings in Alibaba Group and Yahoo! Japan," Bostock said.
"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," he said.
Yahoo! shares were virtually unchanged at $15.83 in after-hours trading that followed the release of Bostock's letter.
The boardroom house cleaning comes just two weeks after Jerry Yang, who co-founded Yahoo! nearly 17 years ago and had an ill-fated stint as chief executive, resigned from all of his positions with the California-based firm.
Yang, 43, one of the original dotcom billionaires, had been on the boards of Yahoo!, Yahoo! Japan and Alibaba Group Holding Ltd.
Yang served as chief executive of Yahoo! from June 2007 to January 2009, during which time he notably turned down a $47 billion takeover bid from Microsoft, earning the ire of many shareholders.
Bostock and Yang have been the targets of stockholder anger as Yahoo!'s stock price sank to about half of what it was when company leaders snubbed Microsoft's generous buyout bid.
Since Carol Bartz stepped down as chief executive in September, Yahoo!'s board has reportedly been looking at selling all or part of the company and Yang was seen as a fierce opponent of a breakup by some shareholders.
Microsoft has reportedly been collaborating with private investors to assemble another multi-billion-dollar offer for Yahoo!.
At least nine private equity firms are also reported to be eyeing Yahoo! and its global audience of 700 million monthly visitors to the company's various websites, including Yahoo! News, Yahoo! Finance and Yahoo! Sports.
Chinese online commerce titan Alibaba is 43 per cent owned by Yahoo! and Alibaba Group chairman Jack Ma has a long-standing offer to buy all or part of the company.
Once seen as the Internet's leading light, Yahoo! has struggled to build a strongly profitable, growing business out of its huge Web presence and global audience.
Yahoo! has popular websites but has been losing advertising business to search giant Google, social networking king Facebook and specialized websites.
Yahoo!'s revenue and net profit dropped in the fourth quarter of 2011, capping off its third straight year of declining results.