The event, on June 23, will be contested over part of the proposed course for the 2014 Commonwealth Games and, with the majority of racing based in the city centre, it will provide a spectacular backdrop for an epic weekend of elite cycling.
UK sports body British Cycling said it received unprecedented interest from towns and cities around the UK, but Glasgow came out top.
Jonny Clay, British Cycling's membership director, said: "In recent years we've seen our national road championships won by riders who between them have won numerous Olympic and world championship medals, as well as the Tour de France.
"The stature of the event and the calibre of the riders who contest it have been reflected in the competition to host the race for 2013.
"We received some great applications and there were several bids."
The event will utilise part of the proposed course for the Glasgow 2014 Games, with most of the racing taking place in the heart of the city, providing a spectacular setting for the title battles, won this year by Sharon Laws and Ian Stannard.
Councillor Archie Graham, the depute leader of Glasgow City Council and the executive member for the Commonwealth Games, said: "There's never been a more exciting time for cycling in Britain, thanks to the outstanding performances of our cyclists at last year's Tour de France and Olympic Games.
"Glasgow is committed to the development of cycling at all levels as shown by our investment in the £113 million Emirates Arena, which includes the Sir Chris Hoy Velodrome.
"Our desire to bring major events such as this and the recent UCI Track Cycling World Cup to the city will help inspire the next generation of cyclists."
The championships will be in the city from June 20, when time trials take place, to June 23 when the men's and women's road races will take centre stage.
The award adds weight to Glasgow's position as a leading destination for hosting major sporting events, with the city also bidding to host the 2018 Youth Olympic Games.
Glasgow 2018 bid team director, Paul Bush, said: "Once again Glasgow is leading the way when it comes to hosting major sporting events.
"Cycling is one of the real success stories of British sport with our cyclists dominating the field in a variety of disciplines and the 2013 Road Race Championships will give the young people of Glasgow the chance to see some of them in action.
"Our bid to bring the 2018 Youth Olympic Games to Glasgow will inspire young people to be champions in their lives and events such as the Road Race Championships will help us on that journey."