Last month was in fact very slightly warmer (0.02 C) than September but the service said they were treating both as joint record-holders.
The data continues Earth's hot streak, with June being the warmest June ever, July the warmest month in recorded history. August was the second hottest August since records began.
Copernicus said its data was further evidence of our planet's "long-term warming trend".
The service, which uses satellite imaging to observe ground-based climate trends, said it had registered significantly hotter than average months for the central and eastern United States, the Mongolian plateau and parts of the Arctic. Temperatures in Europe were lower than the September average, as they were in southwestern parts of Russia and parts of Antarctica.