The 58-year-old Briton beat rival Sergey Bubka, a former Olympic pole vault champion, by 115 votes to 92.
One of Coe’s first tasks will be to deal with the fall-out from a series of doping allegations to hit athletics.
Double Olympic champion Mo Farah and Olympic 1500m silver medallist Steve Cram have both backed their countryman to make a positive impact.
Following his election, Coe tweeted that, after the birth of his children, this was the most “momentous moment” of his life.
The former chairman of London 2012, Coe replaces 82-year-old Senegalese Lamine Diack, who has been in charge for 16 years.