Wessels was six years old when he was introduced to the game of cricket by his sister's boyfriend, Johan Volsteedt. Volsteedt taught him the basics of the game and began to regularly play cricket with him during Sunday visits to the Wessels household. A few years later, Volsteedt became the master in charge of cricket at Grey College, Bloemfontein, and coached Wessels during his playing days for the school's first team.

From a very early age, Wessels showed exceptional sporting talent. By the age of 12, he was playing rugby union for the Free State primary schools team and he was one of the leading schoolboy swimmers in the province. However, after a close encounter with death, due to nephritis, Kepler's father decided that his son would no longer be allowed to participate in swimming.

Wessels decided to switch to cricket, even though the rules of Grey College did not allow him to play at such a young age. With the help of Johan Volsteedt (who was the first team captain), Wessels was allowed to participate in the net practices and soon cricket became his main activity during summer. During winter, he played tennis, at which he won so frequently that, by 1973, he was the number 1 under-16 player in South Africa and was offered a scholarship of $25 000 over four years from the University of Houston. However, due to the fact that he played as an under-16 against adults, Wessels began to lose regularly in senior tournaments. After a dramatic loss during the Griqualand West Open in Kimberley – after which he cut all the strings from his racket in the changing room – Wessels turned down the offer from Houston and decided to focus all his attention on cricket.

As a young cricket player, Wessels scored his first century at the age of nine and was taken into the Free State under-13 side during the same year, getting scores of 80, 80, 88 and 121 against players four years his senior. By the end of 1969, his batting average for Grey College (after nine innings) was 259.59. He was selected to represent the Free State schools side at the prestigious Nuffield Week for five consecutive seasons; and was selected three times for the South African schools side, the third season as captain.

Wessels finished his high school cricket career with an innings of 130 not out, during a home game for Grey College, against rival Queen's College from the Eastern Cape. His superb innings laid the foundation for Grey's first victory over Queen's in 18 years.

He played his first first-class match at the age of 16, batting at number nine and making 32 for Orange Free State in a team captained by the Test veteran Colin Bland. At 18 he was playing professionally in England, opening the batting for Sussex.

In the late 1970s, Wessels was drafted by Kerry Packer to play for the Australian World Series Cricket Team. As a South African with little hope of playing Test cricket for his country, Wessels joined the "circus" to take advantage of the bet