The 62-year-old, who succeeded the now-disgraced Lamine Diack as president four years ago and was standing unopposed for a second four-year term, was voted in at the IAAF Congress in Doha.
The World Championships get under way in the city on Friday with Russian athletes remaining suspended, the IAAF confirmed earlier this week.
It follows the World Anti-Doping Agency's decision to open compliance proceedings against the Russian Anti-Doping Agency.
"It's has been a tough four years, there is no point being naive or coy about that," Coe told the IAAF Congress in Qatar. "The first two years were the reforms. The second two years were making sure they were implemented.
"I am pleased to get here pretty much having implemented everything we said we would do. That is helpful. I want the next four years to be the fun bit. We have to grow the sport.
"We know we have to reach beyond the beltway of athletics fans. We need to form partnerships at every level. We have to place the sport as a service provider for government agendas."
Coe also eased fears ahead of the road events at the World Championships with humidity in Doha around 75 per cent and the temperature still at 33 degrees at midnight.
There are no plans to cancel the marathons with the women's event on Friday night and the men's next Saturday evening, while the race walks are also held at 11.30pm at night.
Coe added: "We have to be mindful of the welfare of the athletes. We have a medical team who will monitor conditions all the time. We've undertaken a lot of work on heat management.
"We recognise the road events are those that need to be carefully monitored. We have more medical supervision, more water available.
"I don't want to speculate, but I want as many people to finish as possible. Heat is not the big issue. The issue is humidity, which is a real challenge.
"We have extra precautions, extra things out on the course. We have more medical supervision, more water available. But it is going to be tough."
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