David Cameron said Helen Glover and Heather Stanning’s victory was “a great success” for the team, while friends and family expressed their pride.
Tour de France winner Bradley Wiggins has become the most successful British Olympian after winning the time trial.
Meanwhile, eight badminton players have been disqualified, officials say.
Glover and Stanning made history by becoming the first British women to win an Olympic gold medal for rowing.
Speaking during a visit to Northern Ireland, Mr Cameron said it was a “great success for the United Kingdom team”.
London Mayor Boris Johnson said an “historic triumph will be celebrated throughout the country today”.
“It’s an outstanding achievement and I’m sure it will spur on all our athletes in the medal stakes. It’s fantastic – Go Team GB,” he added.
In other developments on Wednesday:
- Mr Johnson was left dangling on a zip wire for several minutes when it stopped working at an Olympic live screen event
- Postage stamps featuring Glover and Stanning will go on sale on Thursday
- A Welsh footballer has been suspended after an abusive message was sent to Olympic diver Tom Daley, Port Talbot FC said
- The British men’s eight rowing team, which includes 40-year-old Greg Searle, won a bronze medal while GB men’s rowing quads sculls made Olympic history by reaching their final
- Team GB’s cyclists Emma Pooley and Lizzie Armitstead failed to win a medal in the cycling time trial, as the men’s event gets under way
- GB’s Michael Jamieson and Andrew Willis will compete in the men’s 200m breaststroke, while GB gymnast Dan Purvis aims for a podium finish in the individual all-around event
- London Rail and Tube services were delayed after signal failures on Wednesday morning, while Transport for London warned the Jubilee line would be exceptionally busy in the early evening
Glover, 26, a former PE teacher from Penzance, Cornwall, had been rowing for only four years before securing gold with Stanning, 27, a Royal Artillery captain, from Lossiemouth, Moray.
They stormed home in front of cheering crowds at Eton Dorney after leading from the front in the women’s pair race.
After crossing the line they hugged each other and saluted the crowd, which included princes William and Harry and the Princess Royal.
Speaking at the finish line, Glover’s mother Rachel said her family was “absolutely delighted”.
Stanning is likely to be deployed to Afghanistan next year. Her commanding officer, Lieutenant Colonel Craig Palmer, said: “Soldiers from 32nd Regiment Royal Artillery were thrilled to watch the race from their bases in Afghanistan, while their friends and families watched it here in the UK.
“I am sure that they have been inspired by her performance and we look forward to welcoming her back to the regiment later this year.”
‘Depressing and unacceptable’
In the badminton, four pairs of players – two from South Korea and one each from China and Indonesia – were disqualified after the Badminton World Federation (BWF) accused them of “not using one’s best efforts to win” during games on Tuesday.
Spectators booed the two matches played at Wembley Arena, while some volunteers were in tears.
Speaking at a press conference on Wednesday, Olympics chief Lord Coe said the incident, which saw eight female players apparently attempt to lose, was “depressing”.
“Who wants to sit through something like that?” he said.
“The sadness of it is I was actually at the badminton yesterday and I saw a British competitor narrowly fail to progress but the games were incredibly competitive in front of really large enthusiastic audiences – unacceptable.
“I know the [federation] really well and they will take that really seriously. It is unacceptable.”
South Korea and Indonesia have appealed the decision, the BWF said, with the outcome set to be announced shortly.
The BBC’s Olympics correspondent James Pearce says understands the International Olympic Committee is considering removing the players’ accreditation and expelling them.
London Games’ organiser Locog confirmed it would not refund tickets for the matches.