He is also expected to deal with Ireland's presidency of the European Union, which begins in the new year, at the gathering in Cardiff Castle.
The council was set up under the Good Friday Agreement to foster relations between eight governments and administrations throughout the UK and Ireland.
The latest summit will be the third this year and the 19th since the inaugural meeting in 1999.
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.
The Taoiseach will be accompanied by Children's Minister Frances Fitzgerald who will discuss early years policy.