"I want to achieve a peaceful Chechnya within the Russian federation," Kadyrov, presented with the Chechen flag and coat of arms, told hundreds of guests gathered in a glass pavilion at his Gudermes villa.
Kadyrov, who was nominated by Vladimir Putin, the Russian president, and approved by local parliament last month, is credited by many locals with restoring order after two wars wrecked the region since 1994.
Although Kadyrov is accused of involvement in the disappearances and torture of civilians, allegedly using a private prison at his home in Tsenteroi, in recent years he has also been credited with overseeing a large Moscow-backed rebuilding programme.
Kadyrov, who has always denied allegations of rights abuses, became prime minister in the region's pro-Moscow administration in 2006 and took over as president-designate in February this year.
With the blessing of Vladimir Putin, the Russian president, he has been in de facto control of Chechnya since his father, Akhmad Kadyrov, the then Chechen president, was assassinated in a bomb attack at a sports stadium in 2004.
On Wednesday, in the build up to the ceremony, Suleiman Imurzayev, also known as Khairulla, a Chechen fighter suspected of being behind the bombing that killed Kadyrov's father, died in a shoot out with Chechen security forces killed, Russian media reported.
"This person took responsibility for the death of my father and said that Ramzan Kadyrov is next," Kadyrov said in a statement. "He has now been destroyed."
But on Thursday, the Kommersant newspaper quoted an unnamed prosecution official as saying that Imurzayev had been shot at close range in the stomach followed by a "control shot" to the head, casting doubt on the official claim that he had been killed in a gun battle.
Also ahead of the inauguration Kadyrov, who has cultivated his image as a devout Muslim, made a pilgrimage to Mecca, the Islamic holy city.