Troops on parade for the Queen in Kingston
Hundreds of people lined the streets of the capital Kingston to see the Queen inspect troops of the Caribbean island, of which she is sovereign.
The visit comes just 72 hours after the funeral of the Queen's sister Princess Margaret on Friday.
The trip to Kingston and Montego Bay will be followed by royal tours of New Zealand and Australia, celebrating 50 years since the Queen ascended to the throne.
Commonwealth meeting
The tour had already been postponed once after the terrorist attacks of 11 September and the Queen was determined they would not be put off again despite the death of her younger sister.
The 75-year-old monarch will be travelling abroad for 15 days until 4 March.
The visit to Australia includes the Queen's attendance at the Commonwealth heads of government meeting which was also re-scheduled from October in the wake of 11 September.
Following the ceremonial welcome at Norman Manley Airport in Kingston, the Queen and the Duke laid a wreath at National Heroes Park.
They met Jamaican war veterans, including 108-year-old Eugent Clarke, a survivor of the battle of the Somme in World War I.
He said afterwards: "I am so proud because I never thought that I could see the Queen.
"I fought in the war because England was our mother country and she called for men for service, and I felt in my heart that I should go to England.
"There was no obligation, no conscription - I volunteered."
Later, the royal couple were guests of honour at a reception hosted by the Jamaican Governor General Sir Howard Cooke in King's House.