The body said it had voted to admit the two nations into the elite group that is permitted to play traditional five-day test matches.
As new full members of the ICC, Ireland and Afghanistan will take the total of countries playing tests to 12.
"For a nation like Afghanistan it is a huge and remarkable achievement, the entire nation will be celebrating across all five regions and different provinces. It is the perfect Eid gift," said Afghanistan Cricket Board Chief Executive Shafiq Stanikzai, referring to the approaching Muslim holiday that marks the end of the holy month of Ramadan.
"Everyone has waited for this news and has been so keen to hear this news. Afghanistan cricket has gone from strength to strength and we dared to dream that this would happen and today it has become a reality," he added.
Until 1982 there were only seven full members of the ICC but that year Sri Lanka were admitted. Zimbabwe then joined in 1992 and Bangladesh became the most recent member in 2000.
Cricket has a long history in Afghanistan but the country played amongst the sports minnows until gaining one-day international (ODI) status in 2011.
Two years later, still suffering from the impact of war and conflict, the country was given 'associate member' status of the world governing body ICC.
In 2015 Afghanistan played in their first 50-over World Cup and they have also featured in the World Twenty20 competition.
Ireland have steadily progressed in the game and first qualified for the World Cup in 2007, when they pulled off a shock win over Pakistan, and they have qualified for both World Cups since then.
"We are delighted and proud with today’s historic announcement. It is an extraordinary testament to the talent and endeavour of thousands of passionate players, coaches, volunteers, staff, clubs and committee people," Cricket Ireland Chief Executive Warren Deutrom said.
The ICC conference also agreed on a new revenue-sharing system and voted to expel the United States of America Cricket Association following a series of disputes.
The ICC said it would now work to "establish a new governing body for cricket in the USA that is capable of unifying the fractured cricket community in that part of the world".
(Reporting by Simon Evans; editing by Mitch Phillips and Gareth Jones)
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