Mr Bakiev scored a landslide victory in the poll, winning 89% of the votes.
He had been appointed acting president in March, following the downfall of long-serving former leader Askar Akayev, who fled into exile.
Mr Bakiev, 55, who praised the conduct of the July elections, has said his main goal is to eradicate corruption.
He took the oath of office on the country’s constitution in front of dignitaries in Bishkek’s central square, following a military parade.
Mr Bakiev has said he will expect professionalism from members of his government, who he says will serve on the basis of merit rather than connections.
The president must also seek to improve the economy of a country in which 40% of people live below the poverty line.
Analysts say Kyrgyzstan will have to develop industries such as tourism, hydro-electric power and mining if it is to create new jobs for its 5m citizens.