Coe pipped Ukraine's Sergey Bubka 115-92 in the vote at the International Association of Athletics Federations (IAAF) Congress in Beijing, but he has a tough task ahead of him.
With a series of doping controversies at the top of Coe's agenda when he takes office after the August 22-30 world championships in Beijing, the Briton said he and his new team would be "vigilant" in their crusade against cheats.
"There is a zero tolerance to abuse of doping in my sport and I will maintain that to the very highest level of vigilance," said Coe, who won Olympic 1500m golds in the 1980 and 1984 Games.
"That's something I'm very proud of, that's something I'll very happily defend, how we approached that."
Coe added: "Everything that you do in a sport is underpinned by trust. It's the trust that athletes that are competing feel that they are competing in a free, fair and open environment.
"It's the trust of parents when they are helping their offspring make judgements about the types of sports they go to. They need to know that we are a sport that is very firm in this area."
As part of his candidacy manifesto, Coe had promoted establishing an independent anti-doping body, with IAAF tests currently going through the World Anti-Doping Agency (WADA).
"I'm not really wanting to go into the minutiae of detail at the moment," he said of his plans for the independent body.
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