Amber, 13, went missing on Saturday and her body was discovered last night, less than a mile from her home in Nottinghamshire.
The cause of her death has been confirmed as hanging.
Amber was last seen at home, where she stormed out without her phone or money after an argument.
Superintendent Matthew McFarlane said: "Sadly this was not the outcome that any of us were hoping for.
"Amber's mum and stepdad, Kelly and Danny, would like to say that they were particularly touched by the amazing support they received from the community."
In a statement Kelly and Danny said: "She was never happier than when reading to her younger sisters and being surrounded by her family.
"We will always be grateful for our last family holiday with our beautiful daughter. We will always miss her."
Speaking at a press conference yesterday about the last time he saw Amber, Danny said: "We had all had just a brilliant holiday. It's just not right. We told her to clean a cool box out that we had had sandwiches in for the journey home.
"It was a chore, basically, and I'm sure all teenagers are the same, she didn't want to do a chore. That was the last conversation."