Bostock, who has seen the US web portal fall further behind competitors such as Google during his tenure, will step aside with Vyomesh Joshi, Arthur Kern and Gary Wilson in tow.
Yahoo has been forced to lay off workers four times in the last five years, with share price stagnating around the $15 (£9.50) mark since late 2008. It has also seen four bosses come and go during this period.
PayPal head Scott Thompson took the reins at Yahoo early last month, filling the vacancy left by the outed Carol Bartz. Co-founder Jerry Yang also stepped down from the board in January.
Yahoo's board has been criticised by investors for its inability to land equity investment. The apparent indecisiveness of its shareholders has also come under fire, reports Reuters.
"We have pursued a wide range of discussions with potential partners," Bostock said in a statement.
"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."
Yahoo rejected a $44.6bn (£29.1bn) takeover offer from Microsoft in February 2008.