"These elections have not lived up to the hopes and expectations of the Nigerian people and the process cannot be considered to have been credible, " said van den Berg.
The EU observers called for urgent action over the election, but did not say if it should be cancelled and held again.
Olusegun Obasanjo, the outgoing president, said the polls were "not perfect", but appealed to Nigerians not to lose faith in the democratic process.
He accused "some political leaders" of stirring-up violence and employing thugs to achieve victory, but said Nigerians had shown faith in democracy.
"How many elections on the African continent have ever been fair?"
Mack Rogers, Chattanooga, TN, USA
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Nigeria's main opposition parties rejected the result and said they would take the matter to court over allegations of voter fraud.
Atiku Abubakar of the Action Congress, who is also vice president, and Muhammadu Buhari of the All Nigeria People's Party (ANPP).
Tom Ekimi ,an ANPP official, said both parties "reject the results and we're going to take up the matter legally in court."
The electoral commission said Yar'Adua had won 24,638,063 votes against 6,605,299 for his nearest rival, Muhammadu Buhari.
Atiku Abubakar won 2,637,848 votes the poll said.
The 55-year-old governor of one of the country's northern states is backed by Obasanjo and was the pre-poll favourite.
Atiku Abubakar, the vice president and a former Obasanjo ally, criticised the poll as unfair and undemocratic.
"I have already rejected the elections," said Abubakar before the results were announced, demanding a re-run.
"They have no alternative other than to cancel them altogether."
"What we have seen clearly proves our fears that it is the worst election ever seen," Abubakar said.