Kindler, who quit the giant drugmaker in a surprise announcement three weeks ago, said Wednesday he’ll leave the Fed board tomorrow after just over a year as a director.

Kindler said in his resignation letter, dated last Thursday, that as a former CEO he no longer fills the Fed’s need for “current, high level information about the business environment.”

His term ends in December 2012. The Fed is expected to hold a special election to appoint someone to serve out the rest of Kindler’s term early next year.