It is the second national team job in Africa for the former Kilmarnock and Hibernian boss, who spent five years in charge of Uganda until he was sacked in April last year.
He takes over from Adel Amrouche, fired just hours after Kenya's shock elimination from the African Nations Cup qualifiers on Sunday.
A goalless draw at home in Nairobi in the second leg of their playoff match meant they were eliminated 1-0 on aggregate by tiny Lesotho.
"This is the beginning of a fresh start for our football," Football Kenya Federation president Sam Nyamweya told a news conference.
Details of Williamson's contract will be announced later, he added, saying it would "not be less than two years".
Williamson, 52, has been managing Kenyan champions Gor Mahia, and also had spells in charge of Chester and Plymouth Argyle in England.
(Reporting by Mark Gleeson in Cape Town; Editing by Neville Dalton)
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