They arrived shortly after 10:00 BST by train at Matlock Station and then went to a knitwear company in Lea Mills, before moving on to Chatsworth House.
Crowds including local schoolchildren greeted the royal party at all the venues and they were presented with flowers and gifts.
The Queen previously visited Matlock in 1992, 1985 and 1968.
The Lord-Lieutenant of Derbyshire, William Tucker greeted the royal couple at the station and will accompany them throughout the day.
The Queen and Prince Philip visited the headquarters of John Smedley Ltd, to mark the Derbyshire knitwear company's 230th anniversary.
The Queen was driven to Chatsworth House for lunch with the Duke and Duchess of Devonshire.
In the grounds of the stately home, she was presented with a hamper of local foods and also met staff from the air ambulance, mountain and dog rescue search teams and Peak District park rangers.
Dr Simeon Rayner, from the Derbyshire, Leicestershire and Rutland Air Ambulance, said: "She was very friendly, very engaging. She wanted to know what area we covered so I told her about the counties.
"She also wanted to know whether we had come in a helicopter and I said 'No, we came in a car' but she then told us she was leaving in a helicopter."
The Queen and the Duke of Edinburgh have been cheered by crowds during a visit to the Derbyshire Dales.