Celis was last seen on April 20, 2012, and was reported missing by her father when he realized she was missing from her room the next morning.
One neighbor reported hearing barking dogs outside Isabel's bedroom window at 6:30 a.m. on the day she vanished.
Detectives checked out 2,200 investigative leads, Magnus said.
"Unfortunately, the results of this DNA analysis did confirm that the remains were those of Isabel Celis", Magnus said.
"Although this confirmation may bring some degree of closure, of course it also ends the hope of bringing Isabel home safely to her family", Magnus told reporters at a press conference. Her remains were found in rural Pima County in early March and then sent for DNA testing.
She was last seen by family members when she went to bed at 11 p.m. on a Friday. She was 6 years old at the time.
Magnus would not provide the exact location where the remains were found or disclose what led investigators to Pima County, simply saying that their presence there was "not happenstance".
The Celis family said in a statement: "We want to thank the community for the support they have continued to show for Isa over the years and for refusing to give up hope". Police found "suspicious circumstances around a possible entry point" in the home, leading to the belief that she had been abducted.
Police said they will make the announcement on Friday afternoon.
Magnus did not release many details regarding the girl's remains and their recovery of her body.
There are no suspects in her disappearance. "Now is our time to mourn", the hospital said in a statement.
Magnus wouldn't release any information on potential suspects but he asked the public to contact police with any information relating to Isabel's case. "In fact, reverberations of this have gone well beyond Tucson and even Arizona, (and) have affected people throughout the country", he said. "We believe there may still be folks out there who perhaps know something or feel now that they're willing to come forward with information".