The SpaceX Crew-4 astronaut mission lifted off in the pre-dawn hours of 3:52 a.m. ET from the Kennedy Space Center in Florida. It should arrive at the ISS at 8:15 p.m. ET.
During their 16-hour flight inside a capsule dubbed "freedom," the crew will orbit the Earth around 10 times, according to SpaceX.
"Our heartfelt thank you to every one of you that made this possible. Now let Falcon roar and Freedom ring," radioed NASA astronaut Kjell Lindgren, the commander. Minutes later, their recycled booster had landed on an ocean platform and their capsule was safely orbiting Earth. "It was a great ride," he said.
Onboard the spacecraft are three NASA astronauts, including Lindgren, Pilot Bob Hines, and Mission Specialist Jessica Watkins and the European Space Agency's Mission Specialist Samantha Cristoforetti, NASA said.
The NASA mission is the first with an equal number of men and women and the first long-term flight with a Black woman, Jessica Watkins.
The crew will spend five months at the ISS, replacing three Americans and a German who will return to Earth in a week. Three Russians also live at the space station.
The crew is the fourth to fly on a SpaceX Crew Dragon spacecraft and Falcon 9 rocket, according to NASA. It is the fifth SpaceX flight with NASA astronauts.
The mission was delayed from last weekend because another mission's splashdown was delayed by rough seas, according to Space.com.
The Associated Press contributed to this report.