Craig Clouatre, 40, went missing while hiking with friend Hans Friedmann in Paradise Valley, 80 kms (50 miles) north of Yellowstone on Wednesday.
His remains were found after an “extensive search” by officers from the Park County Search and Rescue team on Friday.
“It appears he had an encounter with a grizzly and unfortunately did not survive,” Park County Sheriff Brad Bichler said in a statement.
“Please keep his family and all those involved in your thoughts and prayers.”
Mr Bichler told the Livingston Enterprise that Mr Clouatre, a keen outdoorsman from Livingston, Montana, had become separated from his hiking companion.
“When the other man returned to their vehicle and his friend wasn’t there, he called us and we began searching.”
In a post on Facebook, Mr Clouatre’s wife Jamie described him as the “the most amazing person” she had ever known.
“I loved him with every single fibre of me,” Ms Clouatre said.
“He was a vital part of me and our children and it is going to be a struggle for the rest of our lives. To say we are broken is an understatement.”
She said she would have to “relearn how to be” to stay strong for their three daughters and son.
The family were familiar with tragedy, having lost “almost everything” in a house fire two years ago, according to a GoFundme page, which had raised more than $63,000 by early Sunday afternoon.
Mr Bichler said he had visited Ms Clouatre on Sunday morning and that the family were still trying to process what had occurred.
“The family understand that Craig loved to be in wild places and was well aware of the risks involved with that,” he said in a social media post.
Mr Clouatre’s father David said his son grew up in Massachusetts and moved more than two decades ago to Montana, where Clouatre met his future wife.
“He was a joy to have as a son all the way around,” David Clouatre said. “He was a good man, a good, hardworking family man.”
The mountains in the area where Craig Clouatre died rise steeply above the Yellowstone River as it passes through the Paradise Valley.
Dense forests at higher elevations are home to bears and other wildlife, although dangerous encounters with people are relatively rare.
Clouatre frequented those mountains and others around the park, hiking in summer and ice climbing in winter when he wasn’t home with his wife and their four young children, said Anne Tanner, a friend of the victim.
Ms Tanner said she had known Clouatre for about a decade because he worked for commercial food companies and delivered to their restaurant, the Emigrant Outpost.
The restaurant held a benefit for the Clouatre family after their house burned down two years ago. Ms Tanner said they had only recently recovered from the fire.
“He was finally just getting their house together,” she said.
“It just makes me angry that something like this could happen to such a good person. Of all the men I know, I can’t believe he would die in the wilderness. He was so strong and he was so smart.”
Since 2010, grizzlies in the Yellowstone region have killed at least eight people.
Associated Press contributed to this report
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