Kenya’s Kipchoge, 35, won the London Marathon for a fourth time in April before becoming the first athlete to run a marathon in under two hours.
He covered the 26.2 miles (42.2km) in one hour 59 minutes 40 seconds in the Ineos 1:59 Challenge in October.
Muhammad, 29, won World Championship 400m hurdles gold in Doha having twice broken the world record this year.
The American, who won the Olympic title at Rio 2016, said: “It’s been an amazing year. It’s been a tough year but I’m so thankful. I never imagined ending the year like this.”
Kipchoge, who won the male athlete of the year award for the second consecutive year, said: “I hope I inspire the human race. I’m just really happy to make history. I hope it was a big inspiration to the next generation.”
Ethiopia’s world 5,000m silver medallist Selemon Barega was named male rising star while Ukraine’s Yaroslava Mahuchikh, who won high jump silver with a world Under-20 record of 2.04m in Doha, won the female award.