A coalition of Conservatives and independents is to replace the previous SNP/Lib Dem/independent alliance.
The Tories won most seats last week with 15, ahead of the SNP on nine, eight independents and two Lib Dems.
The administration has to be officially approved by full council on 18 May. It will see newly elected Conservative Shona Haslam take over as leader from independent David Parker.
Conservative group leader Michelle Ballantyne said she was delighted with the proposed coalition.
"We have worked hard to ensure that our administration will use the skills of its members to deliver the best services for the people of the Borders," she said.
"At last week's local elections, the Scottish Borders voted for change and the new administration will bring a fresh approach to providing that change.
"We have a lot of new members and we are not going to be afraid to use their skills from the outset."
Independent group leader Sandy Aitchison said he was also pleased with the outcome.
"It is fantastic to have 19 new elected members with fresh thinking and new ideas," he said.
"All of us in the new administration are keen to make the most of the new opportunities and energy of the council."
Ms Ballantyne is set to take up a position as a list MSP in the weeks to come but she has yet to decide whether she will continue in her role as a councillor after taking on that post.
Former leader David Parker will move to the role of convener, with responsibility for health.
Ms Ballantyne said: "We are delighted that David will be appointed to the role of convener, a not insignificant position, that is vital for the smooth and effective running of the council.
"David will play an integral part in assisting the new administration in embracing the challenges ahead."
A new administration has been unveiled on Scottish Borders Council.