Kahn's appointment was made at the Annual General Meeting of the Federation in Kuala Lumpur, Malaysia.
The 38-year-old from Karachi in Pakistan, a vice-president for the past four years, succeeds New Zealander Susie Simcock who stands down after serving her maximum terms of six years as vice-president and six as president.
In a close-fought election, Khan beat fellow vice-president Mike Corby, a former British squash and hockey international, to become the Federation's seventh president.
Ex-world champion Jahangir Khan has been elected president of the World Squash Federation (WSF).
