Bourne finished in 10 minutes, 12 seconds and Walsham clocked 12:05 in the race up 86 floors that is described as a vertical marathon, the New York Road Runner (NYRR), which organizes the annual Empire State Building Run-Up, said.
About 600 runners from 18 countries took part in the race, now in its 36th year.
"Obviously I'm very happy to win and it's nice to have all the training pay off," said Bourne. "I wanted to pace myself well and fortunately it paid off."
Four-time champion Walsham was equally elated.
"I had a bear on my back after my crash in 2009 and I trained specifically for this race. It's a personal best time for me and I couldn't be happier," said Walsham who lives in Singapore.
Australian Darren Wilson came in second among the men, followed by Ricky Gates of San Francisco. Brooke Logan of Australia was the second woman to reach the top, ahead of Erika Aklufi, of Los Angeles, who placed third.
German Thomas Dold, the defending men's champion who has won the race a record seven times, did not compete because of illness.
About 30 elite men and women vertical racers, or tower runners, who storm up skyscrapers around the globe, along with fitness enthusiasts and some 200 charity runners ran from the lobby of the landmark building to the Observatory floor.
The elite stair climbers powered up the building first followed by other runners in spaced intervals, according to the organizers.
WORLD CIRCUIT RACE
Many of the top skyscraper racers compete in the Vertical World Circuit, which includes buildings races in Switzerland, Spain, Taiwan, China, Vietnam, Singapore and Brazil. Last month Dold was named the circuit's champion for the fourth time.
Running up tall skyscrapers requires different training and endurance than on a flat surface because of the vertical challenge against gravity, according to experts. During a marathon, runners can pace themselves but running up a building is more like sprinting.
"After about 10 flights you are in oxygen debt," said John Honerkamp, a coach with the NYRR. "For most people they are running (up) 20 to 25 minutes because that is how long it takes them."
The top men usually finish the 1,050-foot (320-meter) climb in 10 to 12 minutes and women about a minute later.
The best way to practice is to hit the stairs and head up. Runners also use the handrails on walls to pull themselves upwards.
Honerkamp explained that for many people climbing up the Empire State Building is a bucket list item to do before they die.
"It is the novelty of it," he said. "It is an extreme sport or task that gets people motivated for various reasons."
Paul Crake of Australia set the course record at 9:33 in 2003. His time was three minutes faster than the winning time of Gary Muhrcke's 12:33 in the inaugural 1978 race. Crake was paralyzed in a cycling accident in 2006.
Andrea Mayr of Austria set the women's record of 11:23.
The Empire State Building Run-up was the brainchild of New York City Marathon founder Fred Lebow.
(Editing by Jill Serjeant and Lisa Shumaker)