The Glaswegian comic's set included jokes about his short stature, and his mum - who was in the audience and screaming with delight at his win - taking in a refugee to their home.
Broadcast live on Radio 4 from the BBC's iconic tent at the Edinburgh Festival Fringe, six competitors performed in the final, in the hopes of winning the top prize. Comedian Mark Watson hosted the show, with the judging panel comprised of Radio 4's Commissioning Editor for Comedy Sioned Wiliam; and comedians Mark Steel and Rachel Parris.
Buchanan - who is performing Purpleberry, his debut stand-up show, at this year's Fringe, is also the Scottish Comedian of the Year runner-up 2017. On winning, Stephen says: "I'm really shocked, it hasn't quite sunk in yet. It's been an incredible experience to take part in this competition - to get to the final and actually win it was amazing. Shout out to my mum who was the one screaming all the way through."
Sioned Wiliam says: "This year's New Comedy Award finalists were all incredibly strong candidates, each with their own distinctive voice. All six performers were wholly deserving of their place in the final. In the end, Stephen impressed us with his wonderfully original material and professional style. It was a faultless performance and he is absolutely a worthy winner. I'm really proud that Radio 4 is able to provide a platform for exciting new comedians to launch their careers, and I'm looking forward to hearing more from all six finalists in the near future."
Mark Watson comments: "It was such a strong final and there's a lot of pressure on all the acts because you're live on Radio 4 and there's a real sense of danger! All of the finalists dealt with it really well. Stephen had a great gig - he was really strong and a very popular winner."
The final will shortly be available to watch on BBC iPlayer and the Red Button.
Previously at home on Radio 2, the BBC New Comedy Award is noted for discovering future stand-up stars. Previous finalists in the competition include Alan Carr, Peter Kay, Lee Mack, Sarah Millican, Russell Howard, Joe Lycett, Josie Long, and Nina Conti.
This year's competition received over 600 entries, with the best 50 selected for regional heats, which took place in June and July in locations in London, Manchester and Cardiff, and were broadcast on BBC Radio 4 Extra.
In addition to the much sought-after accolade, the winner takes home £1,000 and a 15-minute script commission from BBC Studios. The finalists will also be mentored by the BBC Studios comedy team across the year and receive advice, guidance and the chance to write for and appear in slots across the BBC.
Heidi Regan, winner of the BBC New Comedy Award 2017, said: "I'm still coming to terms with how helpful winning the award has been for me. It opened up doors in so many areas and gave me more confidence in my comedy. It was a really fun competition and a wonderful experience all round."
Other recent winners of the BBC New Comedy Award include 2012's Lucy Beaumont, whose third series of To Hull And Back aired on Radio 4 this year; 2013's Steve Bugeja, who has supported Russell Kane on his tour and contributed material to a number of BBC TV and radio comedy shows; 2014's Lee Ridley, who has since found fame by winning Britain's Got Talent; and 2015's Yuriko Kotani, who has supported Joe Lycett and Rob Delaney on tour, and made her TV acting debut in Pls Like on BBC Three in 2017.
For updates, click the button below.