Sheikh Salman beat UAE rival Yousef Al Serkal and Thailand's Worawi Makudi in the first round of voting when he gathered 33 of the 46 ballots to amass the necessary two-thirds majority.
Sheikh Salman is president of the Bahrain Football Association. Human rights groups have accused him of leading a purge of players and officials during Bahrain's violent crackdown on pro-democracy protests in 2011.
He will complete bin Hammam's truncated term, which finishes in 2015. The Qatari stepped down from the post last year after a long battle against claims of bribery and financial mismanagement.
But the build-up to the AFC vote was dominated by claim and counter-claim of outside interference, with the powerful Olympic Council of Asia accused of lobbying on behalf of Sheikh Salman.
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In return, world body FIFA expressed concern over allegations that bin Hammam had also been active behind the scenes, despite being banned from football activities.
Former Saudi Arabian candidate Hafez Ibrahim Al Medlej, who withdrew from the race late on Wednesday, also suggested that FIFA had brought its influence to bear on the process.