There were secret ballots for five positions, with Dai Lloyd of Plaid Cymru elected health committee chair.
Labour's Lynne Neagle will lead the education committee and Conservative Russell George the economy committee.
Conservative AM Nick Ramsay will chair the public accounts committee, scrutinising spending by public bodies.
AMs agreed on Tuesday which party the chairs for each committee would come from, with a Labour AM chairing six of the committees, Plaid Cymru three, the Conservatives two and UKIP one.
Only five of 13 of the assembly's committee chairs were contested. In seven other cases, only one AM was nominated and so there was no ballot.
Scrutiny of the First Minister Committee will be chaired by Ann Jones - the position comes with the job of being deputy presiding officer.
The results of the ballots were:
Those who have been appointed unopposed were:
The committees were divided among the parties based on the number of AMs they have.
Assembly members have voted for the first time to decide who leads some of the body's influential committees.