The appointment on Sunday seals a turbulent succession process that began with the seizure of the seat of government by opposition protestors in March and the flight of the country's first post-Soviet leader.
Bakiyev, 55, swore on the constitution at a formal ceremony surrounded by soldiers and dignitaries gathered in the sun on the capital's central square.
"Taking on the functions of the Kyrgyz Republic's president, I swear before the people and the holy mountains to respect and defend the Kyrgyz Republic's constitution and law, to guarantee the rights and liberties of all citizens, and to fulfil the president's functions ... honourably and tirelessly," Bakiyev said, a cheer going up from the assembled soldiers.
The ceremony marked the final phase in this Central Asian republic's transition from the government of Askar Akayev, who fled as stone-hurling youths overran the White House administration building on 24 March and who now lives in self-imposed exile near Moscow.
Bakiyev won a landslide victory on 10 July, with nearly 90% of the vote. Sunday's ceremony, featuring a pomp-filled military march, cannon fire and traditional Kyrgyz song, was a more media-friendly affair than previous swearing-in ceremonies, which were held behind closed doors.
"Despite... difficulties, we have established democracy and the power of the people. It is our great victory"
Kurmanbek Bakiyev, Kyrgyzstan President
The public was kept away by a police cordon, following a threat by discontented rail workers to disrupt the proceedings. But a crowd of 5000 invited guests attended, including Kyrgyz second world war veterans, bedecked with medals, and representatives of non-governmental organisations.
Neighbouring Kazakhstan's President Nursultan Nazarbayev was the only foreign head of state to attend. Some neighbours, notably Uzbekistan, had voiced alarm over the manner of Akayev's ousting.
In a speech, Bakiyev hailed the occasion as a milestone for this impoverished mountain republic of five million people, which lies on China's western edge.
He restated his constant theme of recent months as he has sought to cement support: The need to fight the country's deep-seated corruption.
"Despite ... difficulties, we have established democracy and the power of the people. It is our great victory," Bakiyev said.
"Above all, our society should regain the principles of decency and honesty that are among the most ancient characteristics of Central Asia. This requires an honest state that works for the good of the people," Bakiyev said. "We will uproot the system of corruption."
This strategically located country hosts both Russian and US airforce units at separate bases near the capital. The US base is used for US-led operations in Afghanistan.
Bakiyev alluded to the challenge that the presence of two rival militaries poses for his government, saying that Kyrgyzstan would "not be a place for the geopolitical games of others".
As president-elect, Bakiyev (R)
met US officials for airbase talks
Moscow remains wary of the US presence in a region long regarded as Russia's sphere of influence.
The speech was welcomed by observers such as Edil Baisalov, head of the Coalition for Democracy and Civil Society, one of many vocal non-governmental organisations in a country known for being less authoritarian than its neighbours. Scepticism
Some groups have voiced doubts about whether Bakiyev's anti-corruption campaign will mean more than pursuing prominent figures from the previous era, such as Akayev's wealthy son-in-law Adil Toigonbayev.
"This speech greatly pleased me - the fact that he addressed us," Baisalov said. "We see the same corrupted figures, the same bureaucrats" as in the Akayev era. "It is time for this to change."
At Sunday's ceremony, Russia was represented by the chairman of the upper house of its Federation Council, while the United States sent Secretary of Commerce Carlos Gutierrez and the Organisation for Security and Cooperation in Europe (OSCE) was represented by its secretary general, Marc Perrin de Brichambaut.