South Africa is the first country to publicly endorse Yar'Adua as Nigeria's new president.
International monitors and Yar'Adua's political rivals have said the elections were flawed to the point of being invalid.
Observers from the European Union said the election was "not credible" and "fell far short of basic international standards".
Yar'Adua claims victory
Yar'Adua has repeatedly said that his election victory is valid and has dismissed criticism of the vote.
"I believe I won this election fair and square," he told the BBC in an interview late on Wednesday.
He also said that if his political opponents disputed the result of the election, they should lodge their complaints with the country's courts.
"Anybody who is aggrieved has the right to seek redress in our law courts and once the law courts pass judgment I will respect whatever judgment the law courts pass," he said.
"If today the election tribunal rules that the election has not complied substantially with the rules, I will willingly accept. But if someone says they want elections cancelled without proper due process I will not agree."
Opposition parties have rejected Yar'Adua's landslide victory and are calling for mass protests on May Day.