Mr Tucker will take over on 1 October, succeeding Douglas Flint who has been in the role since 2010.
The appointment breaks an HSBC tradition of appointing insiders to the chairmanship.
One of his first jobs will be to find a replacement for Stuart Gulliver, the chief executive of HSBC, who plans to step down next year.
While HSBC is Europe's biggest bank, the bulk of its profits are generated in Asia.
Mr Tucker has been chief executive of AIA for seven years, during which he oversaw the insurer's expansion in Asia.
Before AIA, he was the chief executive of insurance giant Prudential, and brings to HSBC his experience at the top of a UK financial giant as well as his Asian exposure.
Richard Dunbar of Aberdeen Asset Management, told the BBC the bank has "obviously decided" that an external perspective would be useful to HSBC at this time.
He added that while chief executive of Prudential, Mr Tucker did a good job of expanding its Asian assets, which are seen as the firm's "jewel in the crown".
HSBC has been through an overhaul in recent years in an attempt to reverse declining profits.
Over the past six years it has cut more than 40,000 jobs and sold off businesses.
Despite those efforts, profits tumbled more than 60% last year.
The banking industry has been hampered by the extended period of very low interest rates, which makes lending money less profitable.
For HSBC, that problem has been compounded by its move into less risky areas of banking since the financial crisis which started in 2007.
Those challenges make the appointment of a new chief executive even more crucial for investors, a search which will now be led by Mr Tucker.
HSBC has also been attempting to repair its image after a series of scandals.
Earlier this year it reached a $470m (Â£325m) settlement with the US government and states related to dubious mortgage lending and foreclosure practices during the financial crisis.
In 2015 Mr Gulliver and Mr Flint apologised for "unacceptable" practices at its Swiss private bank which helped clients to avoid tax.
In late 2012 HSBC paid US authorities $1.9bn in a settlement over money laundering.
AIA said that Ng Keng Hooi, would take over as chief executive from 1 September.
HSBC has appointed Mark Tucker, the chief executive of Asian insurer AIA, as group chairman.