Two first ministers question times will be held each week, one for party leaders and one for backbenchers.
Stephen Flynn has joined the senior ministerial team, while Jenny Gilruth has been appointed deputy FM.
It follows the election of Holyrood's first two trans MSPs - Greens Iris Duane and Q Manivannan - earlier this month.
The SNP leader is to be formally sworn in on Wednesday before he chooses a new cabinet.
Kenneth Gibson has seen off competition from two party rivals and Lib Dem Liam McArthur to land the job.
The MSP for Cunninghame North takes the chair from Alison Johnstone after being elected with 74 votes.
Party leaders sworn in for new term at Scottish Parliament
SNP leader John Swinney was the first to be sworn in following the Scottish Parliamentary election.
Q Manivannan, originally from India, is on a student visa which is due to expire at the end of the year.
