Veteran Russian cosmonaut Oleg Kononenko and his colleague Nikolai Chop, as well as NASA astronaut Laural Ohara Lore, left Russia's Baikonur cosmodrome in Kazakhstan as scheduled at 15:44 GMT with a Soyuz MS-24 rocket.
The Russian space agency announced in a statement that the crew arrived at the International Space Station after 3 hours, AFP reported.
Laural O'Hara Lore, 40, told a news conference in Baikonur: "It's a very special moment and a beautiful feeling to be part of a mission that brought so many people together," according to AFP.
The American astronaut expressed enthusiasm for this first mission in space.
Nicolai Chopp, 39, whose first space flight is also the first mission, said: "The atmosphere is good, and the crew is ready to accomplish the various tasks assigned to them."
The three cosmonauts will replace Russian Sergei Prokobev and Dmitry Petlin and American Frank Rubio, who arrived on the International Space Station a year ago.
Their mission at the station was extended due to damage to the Soyuz MS-22 spacecraft, on which they were supposed to return to Earth, but in December it suffered a massive leak in the coolant during docking with the International Space Station due to a collision with a small meteorite, Moscow said.
The Russian space agency considered at the time that the Soyuz MS-22 was no longer usable except in emergency situations, and decided to send the replacement spacecraft "Soyuz MS-23".
The space sector remains one of the rare areas in which cooperation between Russia and the United States continues, amid high tensions between the two countries over the Ukrainian war.
American Laural O'Hara Lore said Thursday that the International Space Station is a "symbol of peace and cooperation."