More than 50 species of sharks are to be given protection from over-exploitation.
A raft of sharks have been added to the list of protected species.
The requiem shark family includes tiger sharks and small hammerhead sharks.
The trade in fins is pushing the sharks to the edge of extinction.
The vote will give the two shark families a fighting chance of survival.
She said that they know that there's a problem. Over-exploitation for trade is one of the main threats to species.
Cross-border trade in wild plants and animals is regulated by the Convention on International Trade in Threatened Wildlife, which is designed to lower demand for threatened wildlife and allow populations to recover.
New proposals to protect sharks, turtles, songbirds and other species are being debated by countries.
The vote at the 19th Conference of the Parties in Panama will bring the shark fin trade under regulation.
The proposals adopted today for the requiem and hammerhead sharks will forever change how the world's ocean predators are managed and protected.
Half of the trade in shark fins is made up of the two shark families.
To be listed on Cites, a country needs to issue a permit to export and produce a document showing that the trade does not harm wild populations.
The decision needs to be signed off at the end of the meeting, but is not likely to be changed.
The plight of sharks and rays has long been sounded off by conservatoires. Commercial fishing for shark fins and meat is a major factor in their demise.
The health of the ocean is dependent on the health of sharks. Losing them would have a huge impact on other fish populations.
The C Copites 19 is in Panama.
Helen can be followed on social media by using the handlehbriggs.