The 25-year-old soldier, from Middleton, was killed in Woolwich, south-east London, in May.
His commanding officer Lt Col Jim Taylor said in a eulogy that he had been "a true regimental character".
After the service, his body was taken for a private burial at Middleton Cemetery along roads lined by mourners.
The soldier's family, who were greeted by applause as they arrived with his son wearing a T-shirt showing the words 'My Daddy My Hero', 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." (+ video) » | Friday, July 12, 2013
