Residents of the tiny western district of Tain were unable to take part in the December 28 nationwide runoff because not enough ballots were distributed.
A vote was held there on January 2 despite the ruling party's attempts to stop it, and Atta Mills' opposition National Democratic Congress widened its lead from 50.13 per cent of the vote to 50.23 per cent.
Nana Akufo-Addo, the ruling party candidate, had threatened to reject the results but withdrew his court challenges and conceded Saturday.
On Wednesday, Ghanaians attending the inauguration festivities seemed glad that the contest had ended peacefully.
Percy Amoah, 41, said: "I want to see a united Ghana. Whatever happened in the past must be forgotten. I also do not want any Ghanaian child to go to school under a tree".
Most Ghanaians remain among the world's poorest people, earning an average of $3.80 a day.
A tenth of the adult population is unemployed and 40 per cent are illiterate.
Ghana is the world's second largest cocoa producer and the recent discovery of oil is eventually expected to bring in between $2bn and $3bn a year.
But Atta Mills will have to struggle with the effects of a global economic downturn, and the poor are already complaining that wealth is not trickling down.
Atta Mills, 64, served as vice president under Jerry Rawlings, a former coup leader who stepped down in 2001, and will have to dispel any notion his rule will hark back to Rawlings' strongman era.
The election was the third time Atta Mills had run for president.
He spent much of his career teaching at the University of Ghana and served as the country's tax chief under Rawlings.
Atta Mills earned a doctorate from London's School of Oriental and African Studies before becoming a Fulbright scholar at Stanford University in Palo Alto, California.