Sheikh Salman beat Yousuf Al Serkal of the United Arab Emirates and Thai Worawi Makudi in Thursday's vote in Kuala Lumpur, and becomes the successor to the disgraced Qatari Mohamed Bin Hammam, who was banned from football for life by FIFA in 2011.
An AFC statement said: "Sheikh Salman bin Ebrahim Al Khalifa has been elected as the new AFC President following Thursday's election at the AFC Extraordinary Congress.
"Sheikh Salman received 33 of the 46 votes to sweep to victory ahead of Thailand's Worawi Makudi (7 votes) and Yousuf Al Serkal of the UAE (6 votes)."
A fourth candidate, Hafez Al Medlej of Saudi Arabia, withdrew on Wednesday night after gaining little support.
Sheikh Salman will serve a two-year term until the next AFC Congress in 2015.
FIFA president Sepp Blatter said: "I congratulate Shaikh Salman Bin Ibrahim Al Khalifa for his brilliant election to the Presidency of the Asian Football Confederation, as well as to the FIFA Executive Committee.
"One of the key missions he will have to ensure is that unity prevails within the AFC.
"Unity, as well as solidarity, are absolutely key and necessary pillars for any institution to build solid plans and structures for its future.
"With two thirds of the world population, Asia clearly plays a huge role in the international football community. But it certainly has not yet reached its full potential.
"AFC shall unite all its energies to continue to strengthen the growth of the Game in Asia."