Kenyatta took the oath of office Tuesday during a ceremony in Nairobi. He scored a narrow victory against former Prime Minister Raila Odinga.
Museveni, president since 1986, congratulated the Kenyan people Tuesday for Kenyatta's victory. The former deputy prime minister is the fourth president for Kenya since independence from the United Kingdom in 1963.
"I want to salute the Kenyan voters on ... the rejection of the blackmail by the International Criminal Court and those who seek to abuse this institution for their own agenda," the Ugandan president was quoted by Kenyan newspaper The Daily Nation as saying.
Kenyatta and Vice President William Ruto are wanted by the ICC on suspicion of war crimes for violence that followed a disputed Kenyan election in 2007. Odinga's challenge in 2007 sparked political violence that left 1,000 Kenyans dead.
Odinga challenged the 2013 election in the Kenyan high court. There were few reports of political violence during the most recent election.
Museveni said he condemned the 2007 violence, supported the ICC, but suspected it was using its gavel to "install leaders of their choice in Africa and eliminate the ones they do not like."