1) It eliminates legal risk, so drug production becomes instantly a much more lucrative activity, enticing more people to do it.
2) Profits are reduced as the market becomes more competitive.
3) The cartels are unable to pursue their "normal" extralegal means of suppressing competition, because the parties they might seek to suppress now have legal access to state protection.
4) In a competitive, legal market, the successful firms will be the ones which offer the best product - the firms with the best drugs, the highest standards of quality and ethics, the nicest stores, and the best customer service. Why buy from dodgy drug-dealers when you can walk into a beautiful store and get great customer service?
In short term yes, cartels may attempt to protect their monopoly, but in the long term, legalisation dooms them as cultural dinosaurs unable to compete in the new legal, open market.
Edit: This analysis depends upon low taxation. High taxation will still incentivise extralegal selling, but it probably makes the black market a bit safer regardless.