The FT student application will be available internationally through Facebook college groups, where only current college students will see the offer.
Students who use the application will be invited to share it with their friends and the application will identify which of their friends are eligible to receive the free offer.
Ien Cheng, publisher and managing editor of FT.com, said: "There is an increasing demand from university and MBA students for access to the FT's quality of insight and reporting and the new Facebook application will enable them to access that premium content for free.
"This application is part of our ongoing efforts to reach a new generation of readers who we hope will become life long fans of the FT."
Students will be allowed to apply for a free annual subscription a maximum of four times and will be able to display their membership of FT.com on their profile page.
A subscription to FT.com costs £98.99 per year in the UK and $109 in the US.
The launch of the FT student Facebook application comes a week after the paper launched the FT Telecoms, Media and Technology Executive Forum -- an exclusive social network for senior executives in the media, telecoms and technology industries.
In October, FT.com changed its charging model to allow visitors to use its site to access some articles for free.
Rival The Wall Street Journal backtracked on an earlier suggestion that it could end charging online at the WSJ.com. The site now has more than 1m subscribers.