The country has been in a state of crisis since disputed elections in 2011 returned Kabila to office for a second term.
Samy Badibanga will be the country's next prime minister, according to a presidential decree read on state television. Badibanga is the leader of the main opposition bloc in parliament.
DR Congo's former premier Augustin Matata resigned Monday to make way for an opposition figure to take his place following the agreement that was largely boycotted by mainstream opposition leaders.
The deal, which followed a "national dialogue", was aimed at calming soaring political tensions but will extend President Joseph Kabila's term to at least late 2017. He was due to leave office next month.
"The deal currently represents the only roadmap put in place by the Congolese themselves," said Kabila during a defiant speech to parliamentarians in the capital Kinshasa on Tuesday.
He added that he was ready to defend against any attempt to take over the country by force, pledging that elections would be organised in the coming months.
Badibanga's appointment has come as a surprise as Vital Kamerhe, who led the fringe opposition bloc that participated in the national dialogue, had been the favourite to succeed Matata as prime minister.
The country has been in a state of crisis since disputed elections in 2011 returned Kabila to office for a second term. A 2006 constitutional provision limits the presidency to two mandates.
Violent anti-Kabila protests in September triggered by the political instability claimed 53 lives, according to the UN.
Kabila took power in 2001, 10 days after the assassination of his father, the then-president, Laurent Kabila.