He is also expected to deal with the Republic's presidency of the European Union, which begins in the new year, at the gathering which is being held in Cardiff Castle.
The council was set up under the Good Friday Agreement to foster relations between eight governments and administrations throughout Britain and Ireland.
Mr Kenny will also outline Ireland's path to economic recovery with a focus on the close links between the economies of the neighbouring islands, a Government spokeswoman said.
Gangnam tops Bieber's record
South Korean rapper PSY's Gangnam Style has become YouTube's most-viewed video of all time.
YouTube revealed in a posting on its Trends blog that Gangnam Style had been viewed 805 million times by the weekend, surpassing Justin Bieber's Baby, which has had 803 million views.
PSY's video has become a global sensation, with many people around the world mimicking his Gangnam Style dance.
In their October meeting, UN Secretary-General Ban Ki-moon, a South Korean, joked that he had to relinquish his title as "the most famous Korean" and tried a few of PSY's dance moves.