New Nigeria head to take office
In a live broadcast on national television, Obasanjo said Nigeria was a more stable and unified democracy following his eight-year rule.
A two-day strike called by trade unions in protest at alleged electoral fraud received a muted response.
Local and international observers had condemned the polls as "not credible". ------------------------- Changed image
In his farewell address, Obasanjo pledged his support for Yar'Adua and his government, and said he was leaving the country with a strengthened democracy. ------------------------- Can Yar'Adua bring peace to the Delta?
"For the eight years that I have enjoyed your mandate and support, we changed ... the image of our country in the eyes of fair-minded, honest and objective observers both at home and around the world," Obasanjo said. "We have run the longest democratic dispensation and eliminated the risk of violent changes of government through coups and counter-coups in our political culture."
Yar'Adua's inauguration on Tuesday will mark the first time in Nigeria's history that one elected leader has handed power to another.
Obasanjo was elected president in 1999 and served two four-year terms. -------------------------- Surprise holiday
On the first day of the strike in protest against the elections, banks were closed and many school children stayed at home.
The BBC's Fidelis Mbah in the commercial capital, Lagos, said the heavy traffic you would normally see on a Monday was absent.
But it was unclear whether this was due to the strike, says BBC correspondent. Some people may have stayed home because Monday and Tuesday had at the last minute been declared public holidays for the inauguration.
Reuters news agency reports that many Nigerians were apathetic about the protest.
"Tomorrow is the handover, so what difference will it make?" said Daniel Legunsen, who was at work selling photocopiers in Abuja. ------------------------- Unknown quantity
Nigerian Nobel laureate Wole Soyinka has told the BBC the country needs a revolution to break the cycle of incompetent and inhuman leadership.
"I think what a country like Nigeria needs is a genuine, authentic but humane revolution," he said.
Soyinka said Yar'Adua was "an unknown quantity" who was taking power at a "perilous time".
The election commission, Inec, has denied charges that it favored the ruling People's Democratic Party (PDP) during last month's elections.
Mr Yar'Adua won a landslide victory in those polls, according to official results. He has promised to introduce electoral reforms.
The two main opposition candidates have challenged the results in court.