Faure Gna**ingbe was confirmed as the winner of the polls on Tuesday, when the Constitutional Court rejected an opposition claim the poll was rigged.
Security is tight in the capital after violent opposition protests last week.
Mr Faure was initially sworn in after his father's death but international pressure led him to step down.
The BBC's Ebow Godwin in the capital, Lome, says the city is calm and schools have reopened for the first time since last month's elections.
'Irregularities'
The Constitutional Court said the opposition appeal that the election had been rigged, "lacks substance, evidence and merit".
"The court proclaims Faure Gna**ingbe elected president of the republic," said court chairman Atsou-Koffi Amegah.
Thousands have fled Togo since the election
Opposition leader Gilchrist Olympio told the BBC that he rejected the court's ruling and said his party would not join a transitional government, as urged by West African regional grouping Ecowas.
An Ecowas observer told the BBC on Wednesday that he saw "irregularities" during the polling.
Martin a**ogba said that in one polling station in Faure Gna**ingbe's northern stronghold, more ballots were cast than there were registered voters.
However, the official Ecowas delegation says the elections were broadly free and fair, despite a few isolated problems.
Thousands of people have fled Togo for neighbouring Benin and Ghana as a result of the political violence since the election.
At least 22 people died in unrest, mostly in areas of Lome where opposition support is strongest.
The BBC's Elizabeth Blunt, who covered the elections, says Mr Faure is going to need all his charm if he is going to knit Togo back together after an acrimonious campaign and what the opposition believe was a stolen election.
And he also has to woo international donors, especially the European Union which cut off all development aid 12 years ago because of his father's excesses.
