Ian McKeever, 42, was struck down in the freak tragedy as he led a group of hikers up Mount Kilimanjaro, one of many expeditions the experienced adventurer has organised on the Tanzanian peak.
Others in the group - mostly from Ireland - also hit by the lightning storm needed medical treatment for minor burns and shock, but their injuries were not thought to be life-threatening.
Mr Kenny said he was very saddened to hear of the death of Mr McKeever. "I had come to know him over recent years and I admired him not only for his own achievements and charity work but also for his work with young people in challenging them to achieve their full potential," he said.
Mr Kenny recalled getting text updates from Mr McKeever when he led an expedition of students from schools in the Taoiseach's native Castlebar to Kilimanjaro's 5,895m-high summit.
"He was extremely passionate about what he did and driven in his belief that everybody can achieve their potential during their lifetime," he said. "Ian said to me once that there was no place he would rather be than in the mountains. I would like to extend my sympathies to his fiancee Anna and his family, friends and fellow adventurers."
Arrangements are currently being made to make Mr McKeever's remains available to his family, some of whom are travelling to Tanzania. His fiancee Anna was with him during the ill-fated climb.
Mountaineer Pat Falvey, who described the death as a complete and utter freak accident, said his friend was an inspiration to young people, and a dreamer who pushed himself to achieve very difficult goals.
"When I heard it last night I just couldn't believe that it happened where it has," he said. "We've all lost friends in the high mountains, but to feel that he was doing what he was doing, helping and mentoring others to achieve goals, and in such a simple way, to be taken out of it," he said.
A lecturer and broadcaster from Lough Dan in Co Wicklow, Mr McKeever regularly mentored hikers, including many Irish schoolchildren, through his Kilimanjaro Achievers organisation.