The charter flight departed Johannesburg following a frantic 24 hours after the squad was originally scheduled to leave on Sunday, but were held back by a delay in obtaining visas in what was described as an administrative bungle by the South African Football Association (SAFA).
Mkhalele, a former international winger who played 66 times for Bafana Bafana, including at their World Cup debut in France in 1998, will have to follow later after his visa application was initially denied.
"They (the US Consulate General in Johannesburg) refused the visa, but gave no reasons. It is very difficult to deal with the process where you get no information," SAFA president Danny Jordaan told the South African Broadcasting Corporation on Monday.
"We don’t know (why it was denied), we are clutching in the dark, but we hope the matter will be resolved (soon). All of the players are (on the flight) and 99% of the technical staff."
South Africa are due to play Jamaica in a friendly on Friday before taking on Mexico in the showpiece opening match in Mexico City.
"Now we are very happy that we can go to Mexico," South Africa coach Hugo Broos said. "The past days have been a little bit stressful with all the problems we had, but those problems are behind us now and we can focus on what's coming.
"These 10 days go very fast, once we get there we will start working, focusing on the first game against Mexico, so time will pass very quickly. I think everybody is looking forward to starting the World Cup."
South Africa are in Group A and will face the Czech Republic in Atlanta on June 18 and South Korea in Monterrey, Mexico six days later.
They are appearing at their fourth World Cup finals and looking to advance from the group stage for the first time.