One of his main challenges - and there are many - is tackling corruption, which is still widespread in the country despite over six years of fighting it. 
Although President Obasanjo was often criticised for turning his anti-corruption fight into a political witch-hunt, Nigeria has seen some recent success in trying to minimise corruption.
The country is now 18 places above Haiti on Transparency International's global corruption index after occupying last place for years.
Many analysts wonder whether Mr Yar'Adua, a reclusive and mild-mannered Muslim from the conservative north-western Katsina State would have the political will to take on Nigeria's corrupt but very powerful political class.
But Mr Yar'Adua has promised that there would be no sacred cows in his administration's anti-corruption fight.
"If my son or my father is found to be corrupt, they will not be spared," Mr Yar'Adua, a former Chemistry teacher, told the BBC recently.
"We are determined to intensify the war against corruption, more so because corruption is itself central to the spread of poverty," he said shortly after he was sworn in as president.
But does Mr Yar'Adua possess the political will to challenge the corrupt political system that made him president?
Fat contracts
One man who knows the value of political will in fighting corruption in Nigeria is the leader of Nigeria's anti-graft agency, the Economic and Financial Crimes Commission (EFCC).
"Whatever we have achieved in the fight against corruption in Nigeria, it is because we had the political support of the central government," EFCC chairman Nuhu Ribadu told the BBC. 
He is going to be his own man and take even harder decisions than Mr Obasanjo 
Political analyst
"To fight corruption will require a very strong political will on the part of the leadership. Without it, you can't succeed."
There are many Nigerians who question whether Mr Yar'Adua has that will.
They allege that as governor of Katsina, Mr Yar'Adua awarded fat contracts to a company working as a front for his family and say he is not clean enough to lead an honest campaign against corruption.
Mr Yar'Adua denies the allegations.
But his claims to be an honest politician could be weakened by the controversy surrounding the elections which brought him to power.
Local observers have condemned these as a "charade", while European Union monitors said they were "not credible".
Network
But others who claim to know him well say he will surprise Nigerians.
"He is going to be his own man and take even harder decisions than Mr Obasanjo took," Mohammed Haruna, a public affairs analyst and Mr Yar'Adua's former classmate told the BBC News website. 
"Of course, Mr Obasanjo achieved some success with his anti-corruption fight, but the problem was that he picked and chose the people he went after. I don't think Mr Yar'Adua is like that.
Let us give Mr Yar'Adua a chance to prove himself
"I remember Mr Yar'Adua as an honest and just man while we were in university. If he is still anything like that, then I'd say he'd certainly do better than President Obasanjo."
Others point to Mr Yar'Adua's decision in 2003 to drop his deputy Ahmed Jikamshi, following accusations of graft, as evidence of his zero-tolerance for corruption.
Fighting corruption as the head of Nigeria's central government might not be as easy, as the country boasts a network of very powerful politicians and influential business owners who always want to have a say in the way the country is run.
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