The vote followed three turbulent weeks for Sir Ian after his force was found guilty of health and safety failures at the Old Bailey.
The Metropolitan Police has been criticised for endangering the public after innocent Brazilian Jean Charles de Menezes was shot dead by armed officers in July 2005 when they mistook him for a terror suspect.
In the vote, 15 members supported Sir Ian, seven members voted against him and one abstained.
Before the vote, Sir Ian insisted he was a "man of honour" and would have resigned if he believed it was necessary.
Mr de Menezes's cousin, Erionaldo da Silva, said he accepted the decision.
He said: "This not a political issue. It is an issue about the death of an innocent man."