The former mayor of London was joined by Conservative employment minister Priti Patel to argue the case for 'Leave'.
And the former Scottish first minister was joined by former Labour leadership candidate Liz Kendall to argue in favour of 'Remain'.
The 90-minute debate, just nine days before the June 23 vote, was held at YouTube’s central-London HQ in-front of Telegraph subscribers and readers and guests of The Huffington Post UK.
The contest was broadcast live on the websites of both publications as well as on YouTube.
Stephen Hull, the editor-in-chief of The Huffington Post UK said: "We are thrilled to be involved in this historic debate.
"We want to start conversations around the globe on this hugely important moment and encourage Britons, especially first time voters, to make their voice heard."
Chris Evans, the editor of The Daily Telegraph said: "We are delighted to be working with The Huffington Post UK and You Tube to give all our readers and viewers the opportunity to hear both sides of this important argument. This event will be the crucial debate of the referendum campaign."
Stephen Nuttall, the senior director at YouTube, said: "YouTube is a great place to go for information, discussion and debate.
"We're delighted that voters, especially younger ones, will be able to tune in and hear more about these important issues from both sides."
You can watch the EU debate live on the video at the top of this story