Tshisekedi, wearing a blue suit and dark glasses, took the oath of office before his supporters, government officials and foreign ambassadors.
Lingering doubts Congo's powerful Bishops' National Conference, the CENCO, too cast doubt on the presidential election, saying its unofficial tallies from more than 40,000 observers did not match the official results.
"It will be a reconciled Congo, a strong Congo that will be focused on development, peace and security".
Tshisekedi, 55, was proclaimed victor of the presidential ballot on 31 December a year ago with 38.57 percent of the votes, against 34.83 percent of his main opponent, Martin Fayulu Madidi, and 23.84 percent of Emmanuel Ramazani Shadary, the candidate of the coalition led by the ruling party, the PPRD, of the outgoing president, Joseph Kabila Kabange.
"We are committed to working with the new DRC government", State Department spokesman Robert Palladino said in a statement, referring to the country by the acronym for its full name, the Democratic Republic of the Congo.
Many Congolese also believe Tshisekedi is his "father's son" and will put the interest of the country above his own.
Out of the 17 African Heads of State who had been invited, only Kenya's President Uhuru Kenyatta attended the inauguration held in the capital, Kinshasa.
"Some Congolese people are very angry because the leader who they chose did not win the elections", comments Espoir Ngalukiye, a member of LUCHA, a movement of young middle-class activists that started in Goma and has now spread across the country.
Here is a recap on DRC's disputed presidential election.
He will take over from long term leader Joseph Kabila.
Pre-vote favourite, the opposition's Martin Fayulu, took 34.8 percent, it says. While Tshisekedi stayed mostly silent as widespread irregularities and disenfranchisement hollowed out trust in the election, Fayulu denounced them in front of crowds of tens of thousands.
Kabila's chosen successor, Emmanuel Ramazani Shadary, has 23.8 percent. Representatives of Fayulu's coalition were absent, as were leaders of Congo's Catholic Church, to which nearly half the country belongs.
Many African and Western countries, wary that a dispute could reignite unrest in the volatile central African country, have recognised Tshisekedi after Congo's highest court dismissed Fayulu's fraud complaints. Even if Fayulu had been declared the victor "it would have been the same thing", given that Kabila's ruling coalition won a majority of the National Assembly.
The new president will be the first to take power through an election since Congo's independence in 1960, when Prime Minister Patrice Lumumba was toppled in a coup after less than three months in office.
Analysts said the delay in announcing the results had raised suspicions of some kind of "backroom deal" which would benefit Kabila and enable him to influence the new president. Since Tshisekedi's victory was confirmed, their responses have been more muted than those of countries in the region.
He must defuse the anger of Fayulu's supporters, carry out his campaign pledge of ending the "gangrene" of corruption after the Kabila era, and forge a power-sharing arrangement with the outgoing president's bloc.