Mr Barrow said he was stepping down as both council leader and councillor for Oswestry South "with immediate effect".
In a statement, he said he was aware that "the people of Shropshire and my constituents are not getting all they can from me in terms of leadership of the council".
This afternoon Clive Wright, Shropshire Council's chief executive, paid tribute to Mr Barrow, saying he had contributed "an enormous amount of his personal time and a combination of skills and attributes which have shaped the strategy and direction of Shropshire as a whole".
He said Mr Barrow's replacement would be elected at the next meeting of the full council on December 17.
"Earlier this year I informed the local Conservative Association that I would not be standing at the next election and that I would be standing down in due course as Leader of Shropshire Council and as a Councillor.
"In recent weeks I have reflected on my decision to plan my retirement from the Council and on reflection my intention to retire means that the people of Shropshire and my constituents are not getting all they can from me in terms of leadership of the Council.
"Presently the Council is working on its financial strategy up until 2020 and the Leader of the Council should be involved in leading that project and committed to serving as Leader and as a Councillor for that period in my view.
"To have led the Council for such a long time has been a huge challenge and an honour. As my motivation has wavered in recent months however I have decided to announce with immediate effect my decision to stand down from Shropshire Council as Leader and to step down as a Councillor simultaneously to ensure my constituents have the opportunity to elect a new representative and the Council has the leadership it needs for the challenges ahead.
"As Leader I have been proud to contribute ideas, energy and leadership in these the most challenging of financial times for local authorities. During my time as Leader we have seen Council Tax frozen for seven years, the Council has saved £146 million and the new University Centre Shrewsbury has been created and this will help local businesses create jobs and recruit the right skills for Shropshire.
"The decision I have reached is for the good of the Council, the people of Shropshire and my constituents. It is my intention to not comment further and to enjoy a well earned break before embarking on a new challenge in due course.
"Looking towards 2016 the fresh challenges will require fresh eyes and renewed energy. I wish my successor well in meeting and overcoming the challenges ahead for the good of the people of Shropshire."
Mr Wright said: "These are unprecedented times of change and budget cuts for local government, and the enormous pressure upon councillors, particularly the Leader and Cabinet, should not be underestimated.
"Councillor Barrow has contributed an enormous amount of his personal time and a combination of skills and attributes which have shaped the strategy and direction of Shropshire as a whole. In my view the greatest legacy of his strong leadership is University Centre Shrewsbury, which could not have happened without his bold decision-making.
"He has several grandchildren who he dearly loves, and I sincerely hope that by stepping down from the council he will now have the time to enjoy them as fully as I know he would wish.
"This is a good time for change, and it feels like a new era as we shape our strategy for the next five years. There are new opportunities as well as challenges, as the purpose of local authorities will change completely. It will be tough at times, but with a new Leader to be elected at our next meeting of full Council on Thursday 17 December, and the continued enthusiasm of our committed staff working closely with elected councillors, communities and our partners, we will ensure that Shropshire continues to succeed."