The resignation is Thompson's last from a company board. Last week, he also stepped down as a director F5 Networks (Nasdaq: FFIV), the Seattle-based developer of networking appliances.
Separately, Yahoo announced it had sold back a 20 percent stake in China's Alibaba Group for $6.3 billion plus as much as $800 million in new shares when Alibaba goes public. Yahoo had bought into Alibaba under prior management. The deal values Alibaba at $35 billion.
Thompson had worked on that deal which was announced by interim CEO Ross Loewensohn.
Thompson, 54, was forced out of Yahoo, in Sunnyvale, Calif., after only four months after many missteps. The last was his signing proxy materials to the U.S. Securities and Exchange Commission in which he claimed to have received a non-existent degree in computer sciences when he graduated from Stonehill College.
Another Yahoo director, Patti Hart, 56, CEO of Interactive Gaming (NYSE: IGT) also quit as a Yahoo director. Third Point Capital, a New York hedge fund with about 6 percent of Yahoo's shares, disclosed the embellishments as part of its bid to take over Yahoo.
Instead, Yahoo elected three Third Point nominees to its board last week after Thompson, Hart and chairman Roy Bostock quit.
Yahoo shares rose 12 cents to $15.54, valuing the company at $18.9 billion.