Sonko garnered 138,185 votes, while Kenneth came a distant second with 62,504 votes. Bishop Margaret Wanjiru earned 7,654 votes.
The Senator will face off with incumbent Governor Evans Kidero in the August 8 polls.
Earlier on, Kenneth called for a repeat of the nominations, saying the process was not free and fair.
"I disassociate myself from the sham election that Jubilee Party purported to have and demand the same elections be nullified," he said in a statement on Thursday.
The former Gatanga MP complained that some people were allowed to vote despite their names missing in the registers while others were denied the chance.
As of Wednesday night, his competitor Mike Sonko was in the lead.
The party said they had received reports that there were people who infiltrated Nairobi primaries.
Elections board chairman Andrew Musangi said this was the reason most people could not find their names in the registers.
-The Star