The cabinet appointments will be formally approved in parliament on Thursday.
As deputy first minister, Kate Forbes has rejoined the Scottish government.
The previous finance secretary declined to challenge John Swinney for the SNP leadership, and instead was appointed by the newly appointed first minister.
Shona Robison, who stated that she had offered to resign from the position but would be open to accepting a position in the government, will be replaced by her.
In accepting the role, Ms. Forbes expressed her feeling of being "deeply honoured".
After taking his oath of office at the Court of Session, Mr. Swinney is appointing members of his government at Bute House, his official residence.
Ms Forbes, who has spent more than a year as a backbench MSP after stepping down from government in March 2023, had been promised a "significant" role in the government.
In a statement, Ms Robison said she had told Mr Swinney last week she believed stepping down in favour of Ms Forbes would help to bring the SNP together.
"I told you I believed this would strongly signal that for all of us in government, this is the best approach to showing we are united and ready to serve the people of Scotland," Ms Robison said.
"It is also in the best interests of your leadership and for the party; and both of us have always put public duty and the interests of the party over and above any self interest."
In her letter to the first minister, she added: "You have indicated you are keen I remain in government, and I have said I am committed to serve in cabinet in whatever role you see fit."
Mr Swinney, in a written response, said he was "deeply" appreciative of Ms Robison's offer to "step aside from the role".
Several other cabinet members, including Health Secretary Neil Gray, Energy Secretary Mairi McAllan and Education Secretary Jenny Gilruth, have also been seen entering Bute House.
Further announcements are expected on Thursday afternoon.
The cabinet appointments will be formally approved in parliament on Thursday.
Ms Forbes returns to government after more than a year on the backbenches.
She quit government in March 2023 after narrowly losing out to Humza Yousaf in the SNP leadership contest and rejecting a demotion to a rural affairs minister.
The Skye, Lochaber and Badenoch MSP had enjoyed a rapid rise following her election to parliament in 2016, aged 26, becoming Scotland's first female finance secretary in 2020.
After being named deputy first minister, Ms Forbes said: "This is a moment of extraordinary privilege for me. Having previously served in cabinet, I know the duty that all ministers have to reflect the government's priorities and the missions that drive them."
Mr Swinney said Ms Forbes was an "immensely talented politician", adding "her new role will prove critical as we focus on our key commitments of eradicating child poverty, investing in public services and supporting economic growth".