The war left the Korean peninsula divided and people who lived on the northern side were unable to leave.
The two Koreas, which are technically still at war, have organised reunion events before, but this is the first in three years.
The South Koreans were chosen by lottery - the oldest of them is 101.
One woman, aged 92, told reporters she was going to be seeing her son for the first since the end of the war.
Lee Keum-seom said she lost track of her son, then aged four, and her husband in the panic of trying to flee, reported AFP.
"I never imagined this day would come," she said. "I didn't even know if he was alive or not."
Eighty-three North Koreans will be taking part.
The Korean War separated millions of people from their families.
Over the years, at times of relative calm, the two Koreas have arranged for selected groups to visit each other. There have been 20 such events in the past 18 years.
But as those who remember the war grow old, time is running out for many of them.
The group are travelling by bus over the heavily guarded border to Mount Kumgang, one of North Korea's tourist resorts.
They will spend three days in North Korea but only be with their relatives for a few hours each day - in total, only 11 hours. Most of their visit will be heavily supervised.
The event, which is facilitated by the Red Cross, was one outcome of a historic visit between North Korea's Kim Jong-un and South Korean President Moon Jae-in in April.
A total of 100 people were chosen on each side to attend the reunion, but some dropped out after realising the relatives they had hoped to see were no longer alive.