The organizers' ground crew rushed out on the tarmac of the Lambert-St. Louis International Airport when the aircraft, which has four electric engines and a 63-metre wingspan, landed at 06.27am GMT.
"I feel (like) I was coming back from another world," said pilot Bertrand Piccard upon landing.
"It's almost a shock" to return to normal life," Piccardc said.
Despite the long hours "I didn't really feel the fatigue," he said.
"I felt very fortunate to be up there."
The landing was broadcast live on the organizer's website, live.solarimpulse.com.
Piccard departed the Dallas-Fort Worth airport in Texas aboard the Solar Impulse at 09.06am GMT on on the third of a five-stop journey across the United States aimed at showcasing the potential of renewable energy technologies.
St. Louis was chosen as the Midwest stopover to pay homage to aviation pioneer Charles Lindbergh and his "Spirit of St. Louis," the first plane to fly from New York to Paris non-stop.
The Texas-Missouri leg was Piccard's longest flight in the single-seat cockpit to date.
Powerful storms that hit the St. Louis, Missouri area late rendered Solar Impulse's airport hangar unusable, so organizers deployed what they described as a "revolutionary" inflatable mobile hangar.
"We brought the inflatable hangar to the USA for testing purposes and in fact it allowed the mission to stay on schedule," said Andre Borschberg, another Swiss pilot, who co-founded the Solar Impulse project along with Piccard.
The hangar consists of several heavy-duty inflatable segments that attach to each other and can be sealed off like a cocoon.
The mobile hangar is designed to be used at unplanned stops, or at airports unequipped to handle the large solar airplane, said Nils Ryer, head of ground crew operations, in a video on the SolarImpulse YouTube channel.
"It's not that easy to find such a huge hangar," Ryer said. It takes around five hours to set up the hangar, which is "light, easy to use and mainly safe," he said.
The goal of the Solar Impulse project is to showcase what can be accomplished without fossil fuels, and has set as its "ultimate goal" an around-the-world flight in 2015.
The first leg of Solar Impulse's US tour took place on , when Piccard flew the aircraft from the San Francisco, California area to Phoenix.
The US itinerary allows for up to ten days at each stop in order to showcase the plane's technology to the public.
Another stop is planned in the US capital Washington before the trip concludes in New York in early July.
Energy is provided by 12,000 solar cells that power the plane's propellers.
The plane can fly at night by reaching a high elevation of 27,000 feet (8,230 metres) and then gently gliding downward, using almost no power until the sun comes up to begin recharging the solar cells.