Wieland is a medical doctor graduating from Adelaide University in South Australia, but stopped practising medicine in 1986. This was due to an accident Wieland was in with "a fully laden fuel tanker at highway speeds." He endured five and a half months in hospital and has undergone more than fifty operations, as discussed in his book, Walking Through Shadows. He is also the past president of the Christian Medical Fellowship of South Australia.

In 1976 Wieland formed the Creation Science Association (CSA), a South Australian creationist organisation modelled after the Creation Research Society. In 1978 this organisation began publishing a magazine, Ex Nihilo (later called Creation Ex Nihilo), "to explain and promote special creation as a valid scientific explanation of origins." In 1980, CSA merged with a Queensland group to form the Creation Science Foundation, which subsequently became Answers in Genesis (AiG).

In 2005 AiG split as a result of long-standing disagreements between Wieland and Ken Ham, president of AiG. Ham retained leadership of the AiG's United States and United Kingdom branches under the AiG name, while Wieland retained the Australian branch and affiliation with the small Canadian, New Zealand and South African branches, under the name Creation Ministries International.

Today Wieland maintains an active speaking and writing schedule, as well as editing Creation magazine and his role as CEO of CMI Australia.