Burundi's elections, which saw former rebels win a large majority, have been praised by observers and analysts.
Burundians hope the vote means the end of war
Monday's polls passed off peacefully and President Domitien Ndayizeye, whose party came second, has accepted defeat.
The elections are almost the last stage in a peace process to end 12 years of war between Hutu rebels and the Tutsi-dominated army.
"The electoral process was a success," said chief European Union election observer Alan Hutchinson.
The FDD won 58%, with the mainly Hutu Frodebu party coming second with 22% and the Tutsi Uprona party third with 7%, election officials say.
The MPs choose a new president in August, tipped to be FDD leader Pierre Nkurunziza, an ex-university lecturer.
"I appeal to all political parties to accept the people's choice. I ask them to back the election result," said Mr Ndayizeye.
FDD - 59 seats
Frodebu - 24 seats
Uprona - 10 seats
Others - 7 seats
The last time a Hutu won presidential elections, in 1993, the Tutsi-led army staged a coup but correspondents say this is not likely now, as African leaders would not tolerate a military takeover.
"First of all, we need to reinforce national reconciliation so that Burundians can think about a state nation, not a state ethnic group," FDD spokesperson Karenga Ramadhani told the BBC.
Correspondents say the FDD has more Tutsi officials than other mainly Hutu parties and Burundians hope this will mean they can reduce tension between the two communities.
The FDD's biggest challenge is to bring the only remaining rebel group, the FNL into the peace process, observers say.
"It has been an important step forward in the Burundi peace process. But the party which won is facing a lot of challenges," local analyst Zenon Manirakiza said.
Patrick Smith, editor of the UK-based newsletter Africa Confidential, told Reuters news agency that some may not be happy to see former rebels leading the country.
Former rebel leader Pierre Nkurunziza (l) is expected to be Burundi's next leader
"Consolidating it is going to be difficult. It is one of those delicate periods a bit like Liberia or Sierra Leone where people who did heinous things in war now go into government," he said.
The BBC's Rob Walker in Bujumbura says the elections mark a fundamental shift of power in Burundi.
For much of the time since independence, control of the state has been in the hands of a narrow Tutsi elite.
Now, after a peace process lasting five years, the 100 new MPs will take their seats in an assembly, where 40% of seats are reserved for the Tutsi minority and 60% for Hutus.