His sole remaining opponent garnered only 41 of the 465 ballots cast.
Kamerhe told Reuters after his election: "This victory means that I was not only the candidate of my political family ... I was the candidate of everyone."
Kabila's coalition, the Alliance of the Presidential Majority (AMP), won 332 of the 500 seats in the legislature at elections in July, Congo's first democratic polls in more than 40 years.
It took six of the seven parliamentary positions in the ballot which stretched until the early hours of Friday. The remaining post will be decided in a second round of voting on Friday.
The opposition Union for the Nation - a coalition led by former rebel Jean-Pierre Bemba, who lost to Kabila in a presidential runoff in October - had criticised the president's supporters for changing parliamentary bylaws to secure control of influential commissions.
Some opposition legislators said the AMP should have left some posts for small parties by not contesting all seven races.
Kamerhe said: "We allowed democracy to run its course. But we'll work together. I'll have to respond to the needs of both the majority and the minority."
The new parliament will replace a body of appointed government supporters, rebels and civil society members, which helped run Congo during the three-year transition period after the country's war, which ran from 1998 to 2003.
Kamerhe said MPs will begin work as soon as a prime minister is chosen and a new government formed.
Kabila was sworn in this month, promising to unify the country, plagued by decades of mismanagement and the conflict during which an estimated four million Congolese died, mainly from starvation and disease.