The observers said voting had been largely peaceful and thanked Kenyans for turning up at polling stations to choose their leaders.
However, they said complaints about the tallying and transmission of results raised by the opposition National Super Alliance leaders should be investigated by the electoral agency.
They also called for speedy investigations into the killing of IEBC technology boss Chris Msando.
Msando, who was the IEBC data manager, was abducted and killed a few days to the elections. His body was found in Muguga, Kiambu County.
Nasa chiefs said his password was used to hack into the IEBC servers in order to manipulate results, a claim denied by the commission.
Meanwhile, the UK Minister for Africa, Mr Rory Stewart, asked Kenyans to be patient as IEBC verified the results and investigated reports of fraud.
“We urge political parties and candidates to remember that Kenya and Kenyans matter more than any candidate, party or election, and to refrain from actions or statements which could heighten tension whilst the country awaits the vote outcome,” Mr Stewart said.
“Any disputes should be addressed through the established resolution mechanisms, in line with Kenya’s Constitution.”
The observer groups, which held separate press briefings in Nairobi, decried the high number of rejected votes. The number is now above 400,000.
The head of the Carter Centre observer mission, Mr John Kerry, said the group was satisfied with measures put in place by IEBC to conduct credible elections.
“The IEBC has put in place and has thus far followed a detailed process of paper ballot counting and security which, if followed through to the final steps, can give every Kenyan confidence that their vote was properly recorded and therefore this election can appropriately certify the outcome,” the immediate former US Secretary of State said in a statement.
He added that minor variances from established process would not affect the overall integrity and process of the polls.
“IEBC officials and agents were in agreement in most steps; opening and sealing of ballot boxes, what constituted a valid ballot and signing off final tallies of forms 34A by agents,” Mr Kerry said.
“This provides an extensive traceable trail of agreements of many parties on paper ballot process and therefore of outcome, including where party agents were present. In the end, it is the paper ballot that tells the story, not the electronic transmission of numbers.”
He said the Carter Centre expected victors and losers to work within the rule of law and the legitimate dispute resolution mechanisms.
“We affirm with conviction that the judicial process and the election laws of Kenya make full and adequate provisions for accountability in this election. The streets do not,” he said.
Mr Kerry said results transmission was just a tool and the real results were to be found in various forms.
“Do not issue threats. If there is a legitimate complaint, there is a lawful process to deal with it. If there were hackers, were they able to change anything? Validation of results will be determined with checking forms 34A,” he said.
Former Senegalese Prime Minister Aminata Touré, the co-chair of the Carter Centre Mission, lauded the election of three women as governors.
AU head of mission Thabo Mbeki said the polls were largely peaceful.
The former South African president said Nasa flagbearer Raila Odinga petitioned the union about the hacking claim.
“The AU Election Observation Mission has taken note of concerns expressed by some stakeholders relating to tallying of the votes.
The mission calls upon stakeholders to work together to address the concerns, relying especially on the institutions legally established to organise elections, especially the IEBC. We are an AU observer mission and not an AU mission on investigations. That would be an entirely different mandate,” he said.
EU chief observer Maritje Schaake said the courts and the electoral commission should resolve disputes resulting from the polls.
“Soon, names of those who won and those who will be disappointed will be known. It is a sign of leadership to congratulate your opponent with grace,” Ms Maritje said, adding that no Kenyan should die because of elections.