The Queen supported Princess Margaret's children
The three-day visit to Jamaica will be followed by royal tours of New Zealand and Australia.
The Queen and Prince Philip were determined to go ahead with the planned visits, part of which had already been postponed once after the 11 September attacks in the United States.
Princess Margaret's funeral was held at St George's Chapel in Windsor on Friday.
The royal jet was touching down on Monday afternoon at Norman Manley Airport, Kingston.
Following a welcoming ceremony, the Queen and Prince Philip will lay a wreath at National Heroes Park and meet Jamaican war veterans.
Later, the royal couple will be guests of honour at a reception hosted by the Jamaican Governor General in King's House.
On Tuesday, the Queen is due to address a special session of Parliament in Kingston, visit a local primary school and attend a cultural presentation.
Queen mother 'fine'
The couple fly to Montego Bay on Wednesday where engagements include a civic reception and a second speech by the Queen, before attending the Governor General's garden fair.
The Queen Mother, who attended the Friday's funeral despite falling and cutting her arm the day before, is said to be "fine".
A Royal spokeswoman said the 101-year-old was likely to stay at Windsor for some days to recuperate before returning to her Norfolk estate.
The spokeswoman said: "The fact that she was at the funeral means that she is coping wonderfully well."