Rockstar's controversial game - where players commit crime in the fictional city of Los Santos - was presented with the Game of the Year gong at a ceremony in central London.
Sony's The Last of Us also scooped two awards.
Ken Levine - the man behind Bioshock and System Shock 2 - was honoured with a lifetime achievement award.
The Golden Joysticks are the largest publicly-voted video game awards in the world, with this year more than 10 million people casting a vote.
The Lifetime Achievement is a new addition to the ceremony.
Mr Levine has been a high profile figure in the industry ever since he worked with designer Doug Church, on the first-person shooter, Thief: The Dark Project, credited with being one of the first titles to introduce the concept of stealth into video games.
"The great thing about the still-maturing nature of video games is you get to be inspired by the work of novices and veterans alike," he said.
"We're all figuring out day by day exactly what the medium is capable of."
Now in its 31st year, the awards were first given out back in 1983, with the first Game of the Year award going to Jet Pac on the ZX Spectrum.
Andy Robinson, editor of Computer and Videogames, said that three decades on, the awards still "represent the voice of gamers worldwide".
"We've revamped the categories to reflect the diversity of modern gaming and also added the inaugural Lifetime Achievement award, which has made this year's ceremony the most thrilling for us yet," he said.
The Golden Joysticks are not the only big awards for the video games industry.
The British Academy of Film and Television Arts hands out its Video Game Baftas in the spring each year, although the majority of their awards are selected by a panel of experts, rather than a public vote.
Grand Theft Auto 5, released last month, quickly became the fastest selling entertainment product ever, taking just three days to generate $1bn (Â£620m) in revenue.

Seven crews from the New Forest and Dorset battled the blaze in Sopley, Christchurch at 17:41 GMT on Thursday.
Fire officer Sandy Thompson said the firefighters did a "fantastic job in salvaging most of the contents of the house whilst fighting the fire from outside".
The cause of the blaze is not yet known and an investigation is under way.
Derek Slade, a resident of Sopley all his life, called the fire "absolutely terrible".
He said: "We opened the front door and couldn't see across the road for smoke. It was absolutely chaotic.
"I told them I'd get a florescent jacket and stand on the corner to direct the traffic because it was a gridlock.
"Everybody chipped in and sorted it out.
"It gets you choked because it was a lovely place. It's a shock."
Mr Thompson praised neighbours who helped the firefighters.
"Once furniture was removed from the house, several villagers joined in the salvage operation," he said.
"It was a really good effort by all the local neighbours, and the furnishings were moved to a safe outbuilding.
"During the fire the chimney stack had become unstable so it wasn't safe for our crews to fight the fire from inside."
The cause of the fire is not thought to be suspicious.
The adult-themed crime game, Grand Theft Auto 5, has won the top prize at the Golden Joystick awards.
[NEXT_CONCEPT]
Fire crews fought an "intense" blaze in Hampshire after the roof of a thatched cottage caught fire.