She will be occupying the third seat on the Soyuz MS-04 spacecraft when Mr Yurchikhin and Mr Fischer return to Earth in September.
They will travel six hours before docking at the space station.
Roscosmos has reported that two of four Soyuz spacecraft crews will comprise two instead of three members in 2017.
US astronaut Jack Fischer, above, and Russian cosmonaut Fyodor Yurchikhin, crew members of the mission to the International Space Station, ISS, wave near the rocket prior the launch of Soyuz-FG rocket at the Russian leased Baikonur cosmodrome, Kazakhstan, Thursday, April 20, 2017.
At 57, Ms Whitson also is the oldest woman in space. Their first order of business was a congratulatory phone call from family and friends at the Russian mission control center outside of Moscow.
"It's so handsome", Fischer told his wife, describing the experience as "a burrito of awesomeness smothered in awesome sauce". "So no need to miss me".
NASA astronaut Jack Fischer and Russian cosmonaut Fyodor Yurchikhin lifted off from Kazakhstan on Thursday, bound for the International Space Station.
Fischer said he suspected the biggest challenge he faces in his first voyage into space will be learning how to use the station's zero-gravity toilet.
Yurchikhin, 58, has racked up 537 days in space over the course of four missions to the ISS, more than any U.S. astronaut but some way short of the 879 days logged by record-holding compatriot Gennady Padalka.
Ms Whitson, a station commander, is going to become the USA astronaut who has spent the most cumulative time in space - surpassing the 534 days served by Jeff Williams.
The two American astronauts are scheduled to speak with President Donald Trump on Monday.