Shah, who is currently a member of the Armed Forces Tribunal, has been appointed for a period of five years or till he attains the age of 70, whichever is earlier, the Human Resource Development Ministry said in a statement.
"Lt Gen Shah will put in his papers to the Armed Forces Tribunal and is expected to assume duties as Vice-Chancellor shortly," an AMU spokesman said.
Shah, the elder brother of actor Naseeruddin Shah, made it to the top post, beating two other short-listed candidates -- Noor Mohammad, who retired as the Secretary of the National Disaster Management Authority, and Syed Khalid Rizvi, a retired additional DGP of Uttar Pradesh.