The men were the first new arrivals on the space station since the start of the Russian war in Ukraine last month.
Video of one of the cosmonauts taken as the capsule prepared to dock with the space station showed him wearing a blue flight suit.
The yellow uniforms they changed into appeared to be a statement opposing their nation’s invasion of its neighbour.
The standard issue Russian uniform is plain blue, and at least one of the men was seen wearing this before take-off.
Oleg Artemyev was asked about the yellow flight suits when the newly arrived cosmonauts were able to talk to family back on Earth.
He said every crew chooses its own flight suits, so that they are not all the same.
"It became our turn to pick a colour. But in fact, we had accumulated a lot of yellow material so we needed to use it. So that's why we had to wear yellow," he said.
Mr Artemyev, Denis Matveyev and Sergey Korsakov blasted off successfully from the Russia-leased Baikonur launch facility in Kazakhstan in their Soyuz MS-21 spacecraft on Friday.
They smoothly docked at the station just over three hours later, joining two Russians, four Americans and a German on the orbiting outpost.
The three Russians will begin a science mission on the ISS that is set to last just over six months.
Russia’s increasingly aggressive military incursion in Ukraine has resulted in cancelled spacecraft launches and broken contracts, although the ISS is a notable exception.
While many other planned launches have been delayed by the war, the arrival of the three cosmonauts is a continuation of a two-decades-long co-operation between the US and Russia in space.
However, tensions are mounting. Roscosmos chief Dmitry Rogozin has warned that the US would have to use "broomsticks" to fly into space after Russia said it would stop supplying rocket engines to US companies.
Many worry, however, that Mr Rogozin is putting decades of a peaceful off-planet partnership at risk, most notably at the ISS.
NASA administrator Bill Nelson played down Mr Rogozin's comments, telling The Associated Press: "That's just Dmitry Rogozin. He spouts off every now and then. But at the end of the day, he's worked with us.
"The other people that work in the Russian civilian space programme, they're professional. They don't miss a beat with us, American astronauts and American mission control.
"Despite all of that, up in space, we can have a co-operation with our Russian friends, our colleagues."
NASA astronaut Mark Vande Hei, who on Tuesday broke the US single spaceflight record of 340 days, is due to leave the ISS alongside two of his Russian colleagues aboard a Soyuz capsule for a touchdown in Kazakhstan, scheduled for 30 March.
In April, another three NASA astronauts and one Italian are set to blast off for the space station.