The crash that claimed the life of the 58-year-old pharmacist occurred on Sunday near the coal mining town of eMalahleni, 140 kilometres (87 miles) from the South African economic capital.
"Hannes was one of the great locks of his generation and as a member of the Springbok squad from 1995, one of the heroes of our local game," said Alexander.
"He was a hard-working forward who never shied away from getting stuck in and doing the dirty work."
Strydom won 21 caps for South Africa between 1993 and 1997 and played all of his club rugby in South Africa.
The highlight of his international career was helping South Africa defeat New Zealand 15-12 after extra time in the 1995 World Cup final in Johannesburg.
He is the fifth player from the 1995 team to have died after flanker Ruben Kruger, scrum-half Joost van der Westhuizen, and wingers Chester Williams and James Small.
Strydom captained the Johannesburg-based Lions team that won the premier domestic competition, the Currie Cup, in 1999.
