The former England manager quit shortly after Forest were beaten 3-1 by Birmingham at the City Ground.
The club released an official statement shortly after news of McClaren's departure broke, confirming that despite being only three and a half months into a three-year contract, he would not be claiming any compensation.
"He has left the club without compensation - nor will he be seeking any. The club can confirm that the search for a new manager will begin immediately.
"Mr Doughty has also announced his intention to step down as chairman of the club at the end of the season after 10 years in the role.
"The search for a new chairman will commence immediately."