A capacity crowd of about 60,000 saw him shave half a second off the previous best, set in 1999 by Moroccan Hicham El Guerrouj.
Kerr, the Olympic silver medallist in the 1500m, crossed the line in front of a rapturous home crowd in three minutes 42.66 seconds.
He had been targeting the record as part of what he called “Project 222” – the number of seconds he needed to hit to beat the record. His previous best was 3:45.34.
Kerr, 28, ran in a specially designed black suit and running spikes by the running company Brooks.
Pacemakers led the way before dropping out with a lap and a half to go, leaving Kerr with a sprint to the line, well ahead of the rest of the field.
He finished more than three seconds clear of second-placed US athlete Yared Nuguse whose time was 3:45.69.
“It was just incredible, that last lap,” Kerr told the BBC. “It was just me, my shoes and the track. I was absolutely deaf in the last 110 metres.
“I didn’t take my foot off the gas,” he continued, “but… I started to glide and I was like ‘oh wow this feels incredible’. It’s incredible because I’m slowing down.
“So, I was like ‘I better get to the line’. So, crossing the finish line, seeing 42-something – anything – was my goal, so it was great.”
Kerr added: “Today, that was a performance I was able to bring out – I hoped it was going to be a little bit faster, but that’s alright.”
The mile is an event which is not typically run at World Championships or Olympic Games, but in March the former world 1500m champion announced his intention to try to break the men’s mile record.
The feat on Saturday earned him a cheque for $50,000 (£37,000).
His win means the mile record is back in British hands after Roger Bannister famously became the first person to run under four minutes in 1954.
Fellow Britons Steve Cram, Steve Ovett and Sebastian Coe previously held the record, before Algerian Noureddine Morceli set a new best in 1993, followed by El Guerrouj in July 1999.
Keep up with all the latest news from the UK and around the world by following Sky News
Also on Saturday, Olympic champion Keely Hodgkinson was looking to make history in the women’s 800m.
The British runner won the race but had to settle for a time of 1:56.21.
That didn’t threaten the 1:53.28 record of Jarmila Kratochvilova – then running for Czechoslovakia – which she set in July 1983. It is the oldest world record in athletics.
The 43-year record continues with Hodgkinson’s hopes hampered after an accident while cooling down during a training session in Wigan when she tripped over and landed on a metal grate, injuring her knees.