Albanese, 56, will take the helm on April 1. He will replace Mahendra Singh Mehta, whose departure had already been announced.
London-listed Vedanta said it also intended to recommend Albanese as chief executive of Sesa Sterlite Ltd, which groups most of the company's Indian assets.
Albanese, who held the top job at Rio Tinto for almost six years, left in January 2013 after the company revealed a $14 billion writedown almost entirely on the value of his two most significant buys: Alcan and Mozambican coal company Riversdale.
Rio Tinto bought Alcan for $38 billion in 2007, a bruising, top-of-the-market deal made when the company was under pressure from rivals to bulk up or be bought.
Albanese was one of several top mining chief executives who took the blame for their companies' relentless pursuit of growth during the boom years that ended in 2011, and for acquisitions that soured and turned into billions of dollars of writedowns.