Bratton is also the former commander of police forces in New York and Boston.
The appointment further fueled tensions between Prime Minister David Cameron and senior British police officers over who deserved credit for bringing four days of riots under control.
Leaders of the police unions in London don't believe Bratton knows enough about local communities and will just want to use overwhelming force.
"America polices by force. We don't want to do that in this country," said Paul Deller of the Metropolitan Police Federation, which represents more than 30,000 officers in the British capital.
Deller, a 25-year Met officer, accused the government of not being serious about following Bratton's recipe for reducing crime.
"When Mr. Bratton was in New York and Los Angeles, the first thing he did was to increase the number of police on the street, whereas we've got a government that wants to do exactly the opposite," he said, referring to Britain's commitment to slash law enforcement spending as part of debt reduction efforts.
Cameron criticized police tactics as too passive and announced Bratton's hiring on Friday. The 63-year-old resigned as LAPD chief in 2009.
Five people died during the U.K. riots and more than 2,100 people were arrested.
The Associated Press contributed to this report.