In a joint statement, the group of nations said the time had come for a "meaningful, truthful and respectful conversation towards forging a common future based on equity".
It comes after Prime Minister Andy Burnham opened the door to a formal apology on behalf of the UK for its role in the trans-Atlantic slave trade while ruling out the prospect of direct reparations.
"We welcome the agreement of the government of the United Kingdom to engage in a structured, time-bound, inclusive and good-faith dialogue with affected parties addressing the trans-Atlantic trafficking of enslaved Africans and its historical harms," the communique released at the end of the Commonwealth Heads of Government Meeting in Antigua said.
Officials said the time frame for the process would be agreed at a later date, though Foreign Secretary Ed Miliband has suggested it would likely conclude within a year.
Asked whether the government might reach the point of a formal apology by the time it hosted the G20 leaders' summit in Manchester in November 2027, he told the BBC: "Broadly speaking, yes."
Burnham has used his first CHOGM to promise to listen to other member states and pursue a "new approach" to the Commonwealth after the last summit in 2024, saw Downing Street resist calls for an apology and seek instead to focus on the future of the group.
In keeping with his predecessors, he has rejected the idea of paying reparations but has said he wants to look at ways to help poorer countries struggling with debt repayments.
The UK will also allocate Stg40 million ($A77 million) over three years from within existing budgets to speed up critical infrastructure investment including green energy in the Caribbean.
Miliband accused previous governments of having a tendency to "sweep under the carpet" the issue of slavery more broadly and said the previous summit had culminated in a "verbal punch-up", which the government wanted to avoid.
Calls for an apology and reparations have grown in recent years, with St Lucia's Prime Minister Philip J Pierre, chairman of the 15-member Caribbean Community reportedly saying the economic and political bloc was "ready to engage" in the "structured dialogue" that Burnham had proposed.
The Commonwealth leaders' summit coincided with a visit by the King, who is the head of the group, to the Caribbean.
Charles addressed the legacy of slavery as he opened the gathering, telling leaders that it was a "shameful chapter of history", which "fills my heart with horror and my soul with the most profound personal sorrow".
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