CBI members will be asked to endorse Drechsler's appointment at the annual general meeting on July 13.
The CBI president plays a leading role in the organisation's advocacy work, meeting with ministers and senior civil servants, promoting UK business internationally and chairing the CBI Board. It is an unpaid appointment.
Drechsler said: "I look forward to continuing Sir Mike's excellent work with CBI members and politicians to boost jobs and growth across all UK businesses, regions and nations.
"The coming months will be dominated by the prospect of an EU referendum and my focus will be on working with businesses and the Government to champion ambitious reform to ensure the EU delivers for businesses and citizens at home and on the continent."
He added: "While EU reform is top of the agenda, we mustn't lose track of other important growth priorities, including ensuring we have an education system that addresses skills shortages and enables all young people to have fulfilling careers.
"I will also focus on securing the high-quality infrastructure the UK needs to compete on the world stage and ensuring growing firms can access the range of finance options they need to thrive."
Before being appointed chairman of Bibby Line Group Drechsler was chief executive of the privately-owned construction firm Wates Group. He joined Wates in September 2004 and became chairman and chief executive in April 2006 until 2014.
Before this, he worked for ICI, spending the first 10 years of his career on Teesside. That was followed by 14 years holding various positions and living in Brazil, the USA and the Netherlands, which concluded with five years as chief executive of one of ICI's principal international businesses and as a main board director (1998-2003).
He is also chairman of the board of the charity Teach First and chairman of the National Skills Funding Agency. He is a board member of Business in the Community and chairman of its education leadership team.
Drechsler has been a member of the CBI Board since 2012 and was chairman of the CBI Energy Policy Committee between 2007 and 2012 and a member of the chairmen's committee. In February 2015, he received a CBE for services to the construction industry. He graduated from the University of Dublin, Trinity College, with a degree in engineering science. He is married with three children.