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GB scored 113.9 in Strzegom, Poland, with Germany (123.0) in second place and Sweden (148.4) taking bronze.
British rider Nicola Wilson, on Bulana, won bronze in the individual event, with Germany's Ingrid Klimke and Michael Jung taking gold and silver.
GB's Tina Cook was fourth, with Ros Canter fifth and Gemma Tattersall in eighth.
The German team had been in the gold medal position after the dressage event on Friday, before an impressive performance by GB in Saturday's cross-country saw them lead going into the final showjumping stage.
Wilson, Cook and Canter all put in clear rounds to secure GB's first European gold since the 2009 event in Fontainebleau, France.
"I think I'm still pinching myself. It's just been amazing," said Wilson.
Cook added: "We were really wanting that gold, it's been a few years and it's fantastic to be back in this position."
It was a spectacular start for new British performance coach Chris Bartle, the Yorkshireman who left his role with Germany earlier this year after masterminding Olympic, World and European gold medal successes.
"I can't put it into words how impressed I am - I just couldn't be more proud," he said.
"They all rode exactly as they trained and what they're capable of. We now want more golds, for as long as we can."
Leading individual positions after cross-country: 1 Ingrid Klimke (Ger) (Horse: Horseware Hale Bob OLD) 30.30, 2 Michael Jung (Ger) (fischerRocana FST) 32.80, 3 Nicola Watson (GB) (Balana) 35.50, 4 Kristina Cook (GB) (Billy The Red) 38.20, 5 Ros Carter (GB) (Allstar B) 40.20, 6 Kai Ruder (Ger) (Colani Sunrise) 40.30, 7 Sarah Ennis (Ire) (Horseware Stellor Rebound) 43.40, 8 Gemma Tattersall (GB) (Quicklook V) 44.70, 9 Sara Algotsson Ostholt (Swe) (Reality 39) 47.0, 10 Thibaut Vallette Lt Col (Fra) (Qing du  Briot ENE HN) 57.70
Team standings: 1 Great Britain 113.90, 2 Germany 123.0, 3 Sweden 148.40 4 Italy 211.80 5 Ireland 269.20 6 Belgium 286.30 7 Spain 290.10 8 Switzerland 324,10 9 Poland 408.80 10 Belarus 425.50
Great Britain's eventers have won their first European Championships team gold since 2009.