Syngal was heading Gap's Old Navy unit that has been a topic of much speculation after the company scrapped its plan to spin-off the unit in January.
She will replace interim chief Robert Fisher, a member of the founding family behind Gap, who will also step down as chairman of the company's board.
The apparel retailer's shares were down nearly 1.5 percent in extended trading.
Syngal will receive an annual base salary of $1.3 million and will take over effective March 23.
Gap also said existing board member, Bobby Martin, will take on the role of executive chairman and that Elizabeth Smith and Amy Miles will join the company's board from April.
(Reporting by Neha Malara in Bengaluru; Editing by Shounak Dasgupta and Shailesh Kuber)