The 25-year-old soldier, from Middleton, was killed in Woolwich, south-east London, in May.
Fusilier Rigby’s body was guarded overnight during a vigil at the Greater Manchester church by his regiment, the Royal Regiment of Fusiliers.
David Cameron arrived at the funeral with London Mayor Boris Johnson.
The soldier’s family, who were greeted by applause as they arrived at the church, have thanked people “across the world” for their “overwhelming support”.
Fusilier Rigby’s wife Rebecca said:
There are so many kind and generous people out there. It’s just horrible that it takes something such as this to make you see how many good people there are.