The Commission on the Demarcation/Delimitation of States, Provinces and Regions collected a lot of information in 1993 in its purview of trying to create viable, internally consistent, and functional governments. They collected a huge amount of information on who lived where, which cities were primate in certain locales, transport, GDP, and so forth. One was never going to escape the "Gauteng is wealthy as all get out" phenomenon but in terms of breaking up the Transvaal---which was honestly the single most notable development--it was important to rebuild the provinces in a way that would integrate the former homelands without a sense of losing voices or opportunity in a new South Africa. They solicited a lot of proposals, and received many more--some from very technical sources that just looked at metrics and didn't think about politics, and others from very self-interested groups including the various Volkstaat proponents who wanted to carve out a primarily Afrikaans demense and had the right to investigate this under the terms of the interim constitution. The Commission reported back as you can see the PDF (esp. map on p3), recommending nine primary divisions, which was largely followed. They would suggest lower-level regional and local authorities as well later on. There is a "Further Report" that is not there at Wits but may be available elsewhere.
I'll have to look more closely to see about any dissent from the recommendations of the Commission once the measure required approval. But the boundaries are quite close to what became written into law in the 1994 Constitution, under Schedule 1A.
[edit: I assume this is what you mean by "modern provinces," not the 1910 iteration, which is a lot easier but lengthier to discuss.]
The boundaries were drawn up in 1993 by a Demarcation Commission set up as part of the Multi-Party Negotiation Forum (MPNF) leading up to the 1994 elections. The commission started from "planning regions" that the Development Bank of SA set up in the 1980s for economic development planning. These were useful because they were based on functional economic factors and ignored the existing boundaries of the nominally-independent homelands which were to be abolished.
Some changes were made to the planning regions by the commission, and then further changes were made by the party negotiators in the MPNF for largely political reasons. The Interim Constitution (in force 1994-1997) made provision for referenda to change the boundaries in several disputed areas, but in none of these areas were enough petition signatures obtained to trigger a referendum.
Changes were made to the boundaries by constitutional amendments in 2006 and 2009, which resolved some of the boundary disputes and re-opened others. The main remaining dispute is over Matatiele, which is currently located in the Eastern Cape while the vast majority of residents want to be in KwaZulu-Natal.
For more details see: Griggs (1998) The Security Costs of Party-Political Boundary Demarcations: The Case of South Africa. African Security Review, 7(2) pp. 22-32.