The cortege left Chatsworth House for St Peter's Church at Edensor, where a service was held.
The Prince of Wales, who paid tribute to the last of the Mitford sisters who died aged 94 earlier this week, was there with the Duchess of Cornwall.
More than 600 staff from the stately home and hundreds of members of the public lined the route to the church.
The Dowager Duchess of Devonshire's body was laid to rest in a wicker coffin among the Cavendish family graves in the village churchyard.
Chatsworth Garden has been opened to the public for a celebration of her life.
By Aleena NaylorBBC Radio Derby presenter
I understand the dowager duchess attended a funeral herself and there was a wicker coffin at it.
She was absolutely enthralled by the idea.
When someone rather disparagingly said, "Well it looks like a picnic basket," she said, "Well that's what I want."
The order of service for the funeral included hymns, as well as Elvis Presley's How Great Thou Art because of the duchess's love of the singer.
The duchess transformed Chatsworth House in Derbyshire into a popular tourist attraction.
Tributes have been paid all week. Prince Charles said he would "miss her so very much".
The dowager duchess's son Peregrine, the current Duke of Devonshire, said this week his mother had always kept the family together.
"She never complained much about anything. She gets irritated by things but only briefly. Very much a 'half-full' person, optimistic and really happy," he said.
A book of condolences will be available for people to sign in Flora's Temple in Chatsworth Garden.
The Helen's Trust, which supports the terminally ill and the Addington Fund, which helps farming families, were supported by the duchess.
Donations were collected for the two charities.
Chatsworth House, farmyard, stables shops, restaurants and the Chatsworth Estate Farm Shop have been closed for the day.
The funeral of Deborah, the Dowager Duchess of Devonshire, has taken place on the Chatsworth estate.