The 25-year-old fusilier was killed outside Woolwich Barracks in London on 22 May 2013 by Islamist extremists.
His four-year-old son, Jack, was among those at the private ceremony in Middleton Memorial Gardens earlier.
He laid a floral tribute with his mother Rebecca. Its message read: "Me and Mummy Miss and Love You lots and lots. Jack xxx."
Also attending the dedication service for the bronze drum and plaque were Lee Rigby's mother Lyn, step father Ian and father Philip McClure.
The memorial symbolises the service of the drummer and machine gunner who served with the 2nd Battalion the Royal Regiment of Fusiliers.
Col Mike Glover, regimental secretary of the Lancashire Fusiliers, told the ceremony the soldier's death sent "shockwaves through the country."
"The afternoon of May 22 2013 Fusilier Lee Rigby... paid the ultimate sacrifice when the horror of the battlefield was brought to the streets of Woolwich," he said.
"That day will forever be embedded in our nation's history and for many here today it will remain forever in our hearts.
Other service personnel from the borough who lose their lives will also be honoured with a memorial wall in the gardens.
Councillor Peter Williams, deputy leader of Rochdale Council, said: "It is very important that we honour him in a respectful way. We're very proud of him."
Welcoming the memorial, Fusilier Rigby's mother, Lyn, said: "It will be a lovely tribute to Lee who put his life on the line every day to serve his country."
His father, Philip McClure, added: "I am still coming to terms with what happened. Lee will never be forgotten and this memorial is keeping his memory alive in his hometown."
In October, Greenwich Council revealed a stone memorial would be placed in St George's Chapel garden, opposite Woolwich Barracks.
A memorial to murdered soldier Lee Rigby has been unveiled in his home town in Greater Manchester.