Shona Haslam will lead a coalition with independents in running the local authority.
The newly-elected councillor admitted it had been something of a surprise to be selected for the role.
However, she said roads, education, waste management and ensuring the best outcomes for the elderly and young people were areas she would focus on.
Her party won most seats last week with 15, ahead of the SNP on nine, eight independents and two Lib Dems.
The administration will be officially approved by full council on 18 May when Ms Haslam will take up the post previously occupied by independent David Parker.
"It was a bit of a shock to the system but a pleasant shock," she admitted.
"I am really looking forward to the challenge. It is really about doing the day job isn't it?"
She said there were a number of key areas she hoped to tackle.
"It is really about focusing on roads, focusing on education, looking at the waste management situation that is currently in the Borders and looking at outcomes for the elderly and young people," she said.
"These are going to be my key areas that I will be looking at going forward."
Ms Haslam said education and issues surrounding young people would be of particular importance.
"We need to make sure that our schools are absolutely fit for purpose," she said.
"We want to create cathedrals for our children - places where they can learn in an environment that is cutting edge, that they prosper in, that they have room to move and room to breathe."
She said additional and special-needs provision was also a key area, along with caring for vulnerable children.
"One of the things I campaigned on a lot was having a joined-up approach," she said.
"It is really making sure that social work and education and health are all talking to each other about these children and making the children at the centre of decision-making."
Ms Haslam said services should be brought to the child rather than them having to try to access various services.
Meanwhile, Conservative group leader Michelle Ballantyne has confirmed she intends to stand down as a councillor after taking up a role as a list MSP.
"I will probably at some point have to resign my council seat," she said.
"There is a general view that holding two for long periods of time is not appropriate."
The Conservative councillor set to take the helm in the Scottish Borders has outlined her priorities for the region.