Furukawa held a thumbs-up as the rocket charged into low orbit at speeds approaching 14,000 miles per hour (23,000 kilometers per hour), and a soft toy began to float, indicating zero gravity.
"We feel just great," Volkov said in answer to a question from mission control outside Moscow.
The trio will spend almost two days in the cramped Soyuz capsule before docking with the space station, where they will remain until mid-November.
Family, friends and colleagues of the astronauts watched the powerful rocket cast a phosphorous glow over the Russian-leased Baikonur space launch site deep inside the territory of the former Soviet nation at 2:15 a.m. local time (2015 GMT Tuesday).
This is the second run for the revamped version of the Soyuz, which has served as the workhorse of the Russian space program for decades.
While aboard the ISS, the team will witness the final mission of the U.S. shuttle, with NASA retiring the 30-year program after Atlantis flies on July 8.
South Dakota native Fossum, 53, is the oldest member of the outbound crew and has been closely involved with the design and assembly of the International Space Station.
"(I) helped design the space station, I helped build it on two assembly flights, and now to have the opportunity to live there is just amazing," he said before lift-off.
Patrick Buzzard, NASA's representative to Russia, said the two countries have relied and one another over the recent history of space exploration and that nothing was set to change.
"It is such a strong partnership and we have these capabilities that everyone brings to the table. That makes it a more robust program," Buzzard told The Associated Press at the Baikonur launch pad viewing platform.