Becky Dobson, 27, was on holiday with boyfriend Stuart Hill, 30, and his brother Jason Hill, 32, when they were killed in the helicopter crash at 0520 local time [1220 GMT] on Saturday.
The group had been celebrating a birthday and were travelling aboard a Papillon Grand Canyon Helicopters aircraft near Quartermaster Canyon at the famous national park in Arizona, when it crashed and burst into flames.
Three other Britons onboard the helicopter survived the accident and were named as Ellie Milward, 29, Jonathan Udall, 32, and Jennifer Barham, 39.
The group had gone away to celebrate Stuart Hill’s 30th birthday and had saved up for a year for the trip, Mr Hill’s father told the Evening Standard.
The Rev David Hill said his sons were “incredibly close” and called his family “Team Hill”.
“The two brothers loved each other and were very close, and so our misfortune is their support – because they went together, and I will thank God every day for them,” said the Rev Hill.
Peter Dobson, Becky’s father said. “They were always going out and doing things, just enjoyed being with each other. The whole thing is just terrible.”
A witness said he saw flames and black smoke spewing from the crash site, heard explosions and saw victims who were bleeding and badly burned.
“It’s just horrible,” witness Teddy Fujimoto said. “And those victims – she was so badly burned. It’s unimaginable, the pain.”
The Foreign Office has confirmed the deaths and said it is supporting the families of the six people involved in the accident.
“We are in close contact with the US emergency services,” a spokeswoman said.
The three survivors were flown to a hospital in Las Vegas in neighbouring Nevada, where they are currently recuperating.
In a statement reported by local news, Papillon Group chief executive Brenda Halvorson said: “It is with extreme sadness we extend our heartfelt sympathy to the families involved in this accident.
“Our top priority is the care and needs of our passengers and our staff.”
Federal Aviation Administration spokesman Allen Kenitzer said the Eurocopter EC130 crashed in unknown circumstances and sustained heavy damage. An investigation will take place.