His appointment comes as something of a surprise after Prudential's $35.5 billion bid to purchase AIA collapsed earlier this year.
Mr Tucker was chief executive of Prudential between early 2005 and September 2009, after playing a role in the company's Asian operations in the 1990s.
He will replace Mark Wilson in AIA's chief executive position - a job Mr Wilson has been in since 2006 - according to various media reports.
AIG is currently preparing an initial public offering for AIA shares in a stock market flotation that will take place later in the year and is aiming to raise more than $20 billion.
Last month, two of Prudential's top 15 shareholders called for the return of Mr Tucker as the company's chief executive, reported the Financial Times.
They were said to want him to replace Tidjane Thiam following the mishandling of the AIA takeover.
By Asim Shah