Rudolph, 25, who has played 35 Tests and was included in South Africa's provisional World Cup squad, signed a three-year deal with the English county in January even though they already had their allotted two overseas players - Pakistan batsman Younus Khan and Australian pace bowler Jason Gillespie.
The Kolpak ruling is named after Maros Kolpak, a Slovakian handball player, who claimed restraint of trade and won a European court ruling that allowed him to play in Germany.
That ruling is now being applied across all sports and means Rudolph can join Yorkshire (Tykes) without being counted as an overseas player after pledging not to play for his country during that period.
The England and Wales Cricket Board (ECB) approved the signing but said it would continue to work against similar moves which it believes harms the domestic game.
"The ECB have reluctantly agreed to the registration of Jacques Rudolph by Yorkshire, having considered all relevant factors and taken account of the legal implications of the Kolpak decision," the organisation said in a statement.
"The Board in unanimously condemning this type of application are concerned that the registration of players under the Kolpak ruling may not be in the best interests of cricket in England and Wales generally.
"The Board are committed to scrutinising the terms of any such applications carefully and will assess them on their individual merits.
"The Board are committed to continuing to explore all avenues in regard to the tightening and strengthening of existing regulations covering player registration, including lobbying the European Commission through the Arnaut Independent Sports Review"