After the election results, Atta Mills said would be "a president for all".
Election officials announced the result after the last constituency to vote showed him extending his lead over his rival, Nana Akufo-Addo. The electoral commission said the results of the run-off showed Atta Mills had won narrowly with 50.23% of the votes, against 49.77% for Mr Akufo-Addo.
Akufo-Addo´s ruling party conceded defeat after the announcement. It had boycotted the last constituency vote.
Officials say there was no evidence of vote-rigging, as alleged by both sides.
The run-off, with the last vote held in Tain constituency, was closely watched as Ghana remains a rare example of a functioning democracy in West Africa.
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