"We are not going to enter into a public debate with Anderson or his lawyer, " the statement read.
The declaration was made on behalf of all six of Jobs's fellow board members, including Google chief executive Eric Schmidt and former US vice president Al Gore.
"Steve Jobs cooperated fully with Apple's independent investigation and with the government's investigation of stock option grants at Apple," the statement continued.
Anderson made the accusations against Jobs on Tuesday, after signing a deal with the US Securities and Exchange Commission to settle charges about his involvement in the back-dating scandal.
Anderson agreed to pay back US$3.5m received from the grants plus interest, along with US$150,000 in penalties. He will not need to admit to any wrongdoing.
The former CFO had stated that Jobs was fully aware of the practice and the possible consequences, and that Jobs assured Anderson that the options were being granted in a legal manner.
The SEC alleges that the options were, in fact, back-dated and based on fraudulent documents. On Tuesday the SEC brought charges against Anderson and Apple's former general counsel Nancy Heinen.
The board's statement noted that an internal investigation found no wrongdoing by Jobs, and that the SEC cleared Apple from any charges in the case.
However, SEC associate regional director Marc Fagel told VNU that the decision did not apply to individual employees within the company. Fagel declined to discuss whether further charges would be filed.