The South African, 36, replaces Grant Bradburn after winning three trophies in charge of KwaZulu-Natal Inland.
Burger played as an all-rounder for KwaZulu-Natal, Gauteng and Lions and was assistant coach for South Africa A.
“Grant did a fantastic job and it will be my goal to move Scottish Cricket to new heights on and off the field,” he said.
“The opportunity to work with players who have already shown that they can compete with the best in the business is an exciting challenge.”
Acting head coach Toby Bailey will oversee next month’s fixtures with Netherlands, Ireland and hosts Oman and Burger will be in place for Scotland’s home matches against Afghanistan in May, when the Scots will also meet Sri Lanka.
Under Bradburn, who is now Pakistan assistant coach, Scotland reached the World T20 finals and earned first-ever wins over four top-tier sides, including England.
Cricket Scotland CEO Malcolm Cannon commented: “Shane impressed the selection panel not only with his skills and experience but also his passion for the role, his leadership capabilities and people management skills so we very much look forward to welcoming him on board.
“We are looking to build on notable successes against four different full members in the last 18 months, including the historic first ODI win against England last June. We believe that Shane has the skills, energy and ambition to continue that momentum and enable further progress to be made towards our strategic goal of achieving ICC full member status.”