The nuclear disaster drama won best mini-series at the main ceremony on Friday, while it also provided a vehicle for Jared Harris to win best actor for his performance as Soviet scientist Valery Legasov.
The two triumphs were in addition to seven prizes it won at the BAFTA TV Craft Awards earlier this month, which included Johan Renck being named best director.
Sky said the Sister-produced drama has picked-up over 60 awards across the world to date, not least two Golden Globes and 10 Primetime Emmys. Creator Craig Mazin said a massive reunion is being planned in London to celebrate the success.
Zai Bennett, managing director of content at Sky UK and Ireland, said: “We’re incredibly proud that the terrifying true story of Chernobyl is BAFTAs most awarded series in a single year ever.
“As well as highlighting the truly brilliant work of everyone involved in Chernobyl, this recognition reflects the success of our increased investment in original production and fuels Sky’s ambition to make more ground-breaking original TV.”