The Championship kicks off on Friday, 8 June and the flag will fly at Barking Town Hall and the Civic Centre in Dagenham on England match days.
England is in Group D and will take on France on Monday, 11 June, Sweden on Friday, 15 June and Ukraine on Tuesday, 19 June.
Council Leader, Cllr Liam Smith, said: “We wish the England team the best of luck for the UEFA Championship and the St George’s flag will be flown in honour of the team.
“This is a fantastic year for sport and celebrating sporting events is a great way for residents in the borough to come together.
“Barking and Dagenham has a rich sporting heritage and has produced a number of footballing heroes including Sir Alf Ramsey, England Captain Bobby Moore, England Coach Terry Venables, Tony Adams and Martin Peters.
“2012 is proving a very exciting year for sport and we are also proud to be a host borough for London Olympics 2012 which will allow us to build on our already impressive sporting legacy.”