Kenny and Cameron will pay their respects to those who gave their lives at several sites across Flanders in Belgium.
Mr Cameron will use the visit to announce £5m (€6m) in funding to help conserve, repair, and protect First World War memorials and graves across Britain and overseas where British and Commonwealth servicemen and women are buried.
Mr Cameron said: “Next year’s centenary of the start of the First World War will be a time for the whole nation to reflect on the events that saw so many young people of that generation make the ultimate sacrifice.
“Nearly all of us in Britain have some family connection with that conflict, and it is the many millions of small, personal stories that resonate as loudly for us as the big, world-changing battles and campaigns.
“As part of that, it is absolutely right that we help communities up and down the country to ensure that their local war memorials are a fitting tribute to the fallen and increase people’s understanding.”
Announcing the joint visit last month, Mr Kenny said that, following Queen Elizabeth’s visit to Dublin in 2011, he and Mr Cameron had been keen to mark the sacrifice of those killed, missing, or injured on the battlefield.
He said: “When Queen Elizabeth visited the Republic, the first visit by a reigning monarch in a hundred years, she closed a circle of history and recognised in so many deep ways the story of 50,000 soldiers from the Republic who fought with the Allies in World War One.”
The leaders will visit the Irish Peace Park at Messines, a memorial to the 50,000 Irish war dead, before travelling to the grave of William Redmond, nationalist politician and Member of Parliament in the Irish Parliamentary party.
Redmond was commissioned as a captain in the Royal Irish Regiment, with whom he served 33 years, and went to France with the 16th (Irish) Division, in 1915.
In response to the execution of the leaders of the 1916 Easter Rising, Redmond requested that, in the event of his death, his grave be located outside the walls of the British military cemetery at Locre. This wish was granted.
Afterwards, they will visit the village of Wytschaete, where the 16th (Dublin) and 36th (Ulster) divisions advanced in the bloody 1917 Messines Ridge offensive.