Wikipedia gives no examples of written mentions from ancient times because there are none. And by the time written records arrive what they record is not really "discovered".
Ancient seafarers likely did have operational knowledge of ocean currents, i.e. they made use of them, but they left nothing in writing about it, at least nothing that survived. For example, it is often inferred from the pattern of colonization of Polynesian islands that pre-historic Polynesians had working knowledge of currents. But they had no written language and only made stick charts. Here is another typical inference in Gugliotta's Trailing Ancient Mariners from artifact similarities in Synope (modern Turkey) and Crimea (modern Ukraine) c. 5000 BC:
"Along the coast, whether in Synope or modern Ukraine or Russia, artifacts showed remarkable similarities. Roof tiles in the Crimea were stamped with the Greek word "Synope," and studies of ocean currents and winds showed that sailors could travel the 180-mile south-north route across the sea from Synope to the Crimea, and probably did."
That ancient Phoenicians knew of the Canary current is similarly inferred, see e.g. Ecohistory of the Canary Islands by Crosby.
As far as the written record, timelines typically start with Ben Franklin naming Gulf Stream that and mapping it in 1769, see HISTOCEA's History of Oceanography, or even with US Navy officer Maury starting a systematic data gathering on currents in 1842, see The History of Measuring Ocean Currents by Joseph. Maury was extracting information from already existing ship logs, and was slightly predated by Dana, who sailed under captain Wilkes in 1838-42 and undertook systematic studies of Antarctic currents. So it was a surprise that Carta Marina published by Olaus Magnus in 1539 already had an accurate depiction of currents near Iceland, see Ancient map captures ocean front by Kettlewell:
"Most of the northeast Atlantic is drawn using more-or-less straight lines. However, things change off the east coast of Iceland, where the lines suddenly morph into a large group of whorls. "Their location, size and spacing seem too deliberate to be purely artistic expression," Tom Rossby told BBC News Online. "Nowhere else on the chart do these whorls appear in such a systematic fashion."
When oceanographers from the UK's Plymouth Marine Laboratory and the University of Rhode Island compared these whorls with thermal images from an Earth observation satellite, they saw something surprising.
Magnus's whorls corresponded almost perfectly with the Iceland-Faroes Front - where the Gulf Stream meets cold waters coming down from the Arctic. "They are the earliest known description of large-scale eddies in the ocean - these are huge bodies of water, 100km in diameter, that turn slowly," Professor Rossby said.
"It seems the lines were deliberately drawn to aid navigation.""