The historic Axiom 1 mission crew docked to the International Space Station's (ISS) Harmony module space-facing port on Saturday morning following delays.
Soft capture was confirmed at 8:29 a.m. ET and docking was reported as "complete" at 8:41 a.m. ET.
The Crew Dragon Endeavour was initially expected to dock at 7:45 a.m. ET, but it was held 20 meters away from the station as the station crew worked to troubleshoot the problem.
NASA's live broadcast said the crew could have remained parked in that position for about two hours.
The Dragon Endeavour hatch, which was previously expected to open at around 9:30 a.m. ET, opened at 10:13 a.m. ET.
The crew of the 10-day flight includes former NASA astronaut Michael López-Alegría and paying passengers Larry Connor, Mark Pathy and Eytan Stibbe. The three businessmen paid $55 million apiece.
The astronauts will take part in a multi-discipline science program, including a thunderstorm observation experiment first begun by Ilan Ramon, who died aboard shuttle Columbia in 2003.
"They’re not up there to paste their nose on the window," Axiom’s co-founder and president, Michael Suffredini, a former NASA space station program manager, said in a statement.
They join Expedition 67 crew members, including NASA astronauts Thomas Marshburn, Raja Chari and Kayla Barron, European Space Agency (ESA) astronaut Matthias Maurer and Roscosmos cosmonauts Oleg Artemyev, Sergey Korsokov and Denis Matveev.
NASA said the mission represents both "a culmination of NASA’s efforts to foster a commercial market in low-Earth orbit and a beginning of a new era of space exploration that enables more people to fly on more kinds of missions."
Friday's flight is the second private charter for SpaceX, which took a billionaire and his guests on a three-day orbit ride last year.
Axiom Space is targeting next year for its second private flight to the space station.
The Associated Press contributed to this report.