Odinga (left) challenged the declaration of Kenyatta as the victor of the presidential election by the Board.
Justice Philomena Mwilu said that the Independent Electoral and Boundaries Commission's (IEBC) refusal to provide access left the court "no choice but to accept the petitioner's claims that the IEBC's IT system was infiltrated and compromised, and the data therein interfered with, or IEBC's officials themselves interfered with the data".
The Supreme Court has held IEBC chairman Wafula Chebukati responsible for playing a role in bungling the August 8 presidential election.
The decision to annul the election was an unprecedented move in Africa where governments often hold power over judges.
A non-governmental organization on Monday filed two petitions claiming judges had improper contact with lawyers for opposition leader Raila Odinga during his court challenge of Kenyatta's win.
Western diplomats have expressed their concern at the rising tensions in Kenya, urging politicians not to incite violence.
Separately, a French company that provided equipment for last month's elections says the biometric and results transmission equipment would not be ready for the new vote next month because it would have to be reinstalled.
Jubilee supporters in Nyeri town demanded the Supreme Court to order recount of votes of the presidential elections.
The IEBC blamed network failures for missing and delayed tally forms, but the judges dismissed this excuse saying they should have been prepared, and that it should have taken only a few hours to get to a spot with enough connection to scan through the forms.
The presidential results announced on August 11 were based on forms which were not the primary document that the law says should be used to compile presidential elections results and some of those forms were of "dubious authenticity", said the judgment.
The board overseeing the 2017 vote did not have all the tally forms when it announced results, and some forms lacked security features like water marks, signatures or serial numbers, which calls their authenticity into question, the court said, adding there was no evidence of individual wrongdoing.
The election re-run has divided Kenya, with many opposition supporters celebrating it and the president and some members of the ruling party criticising it harshly.
Maraga said at a news conference Tuesday that the justices have been receiving "aggressive" threats since they issued their ruling. "We clearly have a problem", Mr Kenyatta said of the judiciary.
The roads around Kenya's Supreme Court were cordoned off Wednesday, and police dispersed protesters from the ruling and opposition parties who had gathered outside.
When making the earth-shaking judgment annulling the presidential election, Chief Justice David Maraga had said that the judges had found "irregularities and illegalities" in the conduct of the election.