• Keith Brown has been the MSP for Ochil Constituency since May 2007
Mr Brown moves from his post as minister for skills and lifelong learning to take over responsibility for transport and infrastructure in Mr Salmond's SNP Scottish Government.
The reshuffle hands control of the climate change remit, which was part of Mr Stevenson's brief, to Environment Minister Roseanna Cunningham.
SNP backbencher Angela Constance was named as Mr Salmond's choice to take on skills and lifelong learning, which needs parliamentary approval.
Finance Secretary John Swinney is expected take the lead on transport issues for the next few days to give Mr Brown a chance to get up to speed.
Mr Stevenson quit his job on Saturday following fierce criticism of his handling of the weather chaos which saw hundreds of motorists stranded overnight on gridlocked roads.
Mr Salmond said: "Keith Brown has been an excellent minister for skills and lifelong learning, and has all of the qualities needed to help meet the unprecedented challenges thrown up by the recent severe winter weather, as well as preparing for future challenges.
"Finance Secretary John Swinney will take the lead on transport issues for the next few days, and under John's leadership, I am confident that Keith will play a key role in ensuring that our infrastructure and transport can stand the extremities whatever the weather might throw at us in Scotland.
"Angela Constance has proved herself to be an extremely able parliamentary performer in committee and in debates in the chamber, which is why I intend to bring her into the Government.
"Angela will be a real asset to the Government in the skills and lifelong learning brief which Keith has filled so ably, and along with Michael Russelll will help drive forward the improvements we are seeing across the board in Scotland's classrooms.
"Tackling climate change is a key priority for this Government, and we are proud to have passed world-leading legislation on this issue. And in order to ensure the policy remains a top focus of this administration it has now been combined with the Environment portfolio under Roseanna Cunningham."
Mr Brown said: "Stewart Stevenson can be proud of his achievement in piloting world-leading climate legislation through the Scottish Parliament, and has made a real contribution to the success of the Scottish Government in the last three and a half years.
"I have enjoyed making a positive contribution to Scotland's education system as minister for skills and lifelong learning, including the introduction of the Curriculum for Excellence, and I am looking forward to taking on the job of Minister for Transport and Infrastructure, with all the challenges that involves."
Keith Brown has been the MSP for Ochil Constituency since May 2007.
Before his election he served for 11 years as a councillor in Clackmannanshire, and held the post of Council Leader from 1999 to 2003.
He has also been since 1999 a member of the European Union's Committee of the Regions, serving as President (2004-2006) of the Union for a Europe of the Nations - European Alliance (UEN-EA) group on that body.
Mr Brown worked for 15 years as a local government professional in neighbouring Stirling, where he was also an active trade union representative with UNISON.
He is a graduate of Dundee University and a former Marine who served in the Falklands. Originally from Edinburgh, Mr Brown now lives in Dollar with his three children.