KAMPALA, Uganda — Commonwealth leaders agreed to a historic reform yesterday by formally dropping the requirement for members to be former British colonies.

The decision came on the last day of the Commonwealth summit in Uganda’s capital Kampala. For the first time, the 52 member states set down conditions for membership. The Commonwealth’s origins were devised at conferences held in the early 20th century by British Empire prime ministers in London.

But numerous countries with no links to Britain are expressing an interest in joining. They include Rwanda, colonized by Germany and then Belgium, which dropped French as its official language and will probably be admitted at the next summit in 2009.

Former French colonies such as Algeria and Madagascar have also told the outgoing secretary-general, Don McKinnon, that they would like to join. So has East Timor, a former Portuguese colony.

In their final communiqué, Commonwealth leaders said an “applicant country should, as a general rule, have had an historic constitutional association with an existing Commonwealth member.”

The summit reaffirmed, however, that all new members must acknowledge Queen Elizabeth as head of the Commonwealth and use English for all official communications.

So far, Mozambique is the only Commonwealth member with no history of British rule.

Nelson Mandela, then South Africa’s president, successfully championed its application to join in 1995. At the time, this was attributed to Mr. Mandela’s unique authority.