Chebukati spoke moments after the Supreme Court delivered their judgement.
In a statement, Chebukati said the commission welcomed the determination by the Supreme Court in its Monday judgement.
"The unanimous Determination by the Honourable Court affirms our resolve and deliberate efforts to conduct free, fair and credible elections.
We await the reasoned judgement to inform our post-election evaluation that is about to commence; as well as initiatives focused on developing our institution and enhancing internal democracy," Chebukati said in the statement.
In its ruling, the court unanimously determined that the two petitions filed by Former Kilome MP Harun Mwau, activist Activist Njonjo Mue and a voter Khelef Khalifa were not merited.
The ruling now paves way for President-elect Uhuru Kenyatta to be sworn in next week on Tuesday according to the constitution.
Chebukati declared President Uhuru Kenyatta as the winner of the October 26 repeat polls.
While announcing the final tally in Nairobi, Chebukati said Kenyatta garnered 7,483,895 votes or 98.2 percent of all validly cast votes.
He placed the national total voter turn at 38.3 percent, and declared that the commission was satisfied the elections “were free and fair”.