Scheib's body was found Sunday night after a weeklong search that started when his girlfriend reported him missing. He failed to return from a June 13 hike in the mountains near the Taos Ski Valley.
Authorities have yet to determine the cause of his death. Investigators were combing the area for clues Monday while waiting for a preliminary autopsy report.
Scheib recently moved from Florida to Taos. He was 61.
He spent 11 years leading the White House kitchen under Presidents Bill Clinton and George W. Bush. He was in charge of a full-time staff of five and oversaw a part-time staff of 20.
Scheib was known for refocusing the White House kitchen on distinctly American cuisine with seasonal ingredients and contemporary flavours. He was responsible for preparing everything from First Family meals to formal State Dinners.
Both presidential families released statements Monday saying they were saddened by his tragic death.
Laura Bush called Scheib an outstanding talent, referring to his many magnificent dinners. Bill Clinton said his family was grateful to have Scheib with them in the White House for six years.
"Walter used his immense talents not only to represent the very best of American cuisine to visiting leaders, but to make a difference in people's lives across the country through his support of numerous charities," Clinton said.
Scheib's creations were served to many world leaders including Tony Blair, Jacques Chirac, Vicente Fox, Nelson Mandela and Boris Yeltsin.
A graduate of New York's Culinary Institute of America in 1979, Scheib went on to work at grand hotels in Florida and West Virginia before becoming White House executive chef in 1994.
Last month, Scheib cooked dinner for a cancer charity's fundraiser at a hotel in Scranton, Pennsylvania. He told the Times Leader newspaper that preparing meals at the White House had required him to have a different outlook on food and cooking.
"When you're working at the White House, it's not a hotel or a restaurant or a private club. It's a personal home," Scheib said. "Our goal wasn't just to cook food at the White House, it was to give the First Family an island of normal in a very, very crazy world."
Scheib left the White House in 2005. He became a food consultant and speaker, often entertaining guests with anecdotes from his time at the White House. He also wrote a book about his experiences entitled "White House Chef: Eleven Years, Two Presidents, One Kitchen."
Scheib also was involved in Atlanta's City of Refuge, which provides services to the homeless and victims of substance and physical abuse. He had assumed the role of chief culinary officer earlier this year, taught culinary students at the centre and helped to open a bistro on its campus.
"We are unbelievably saddened that our friend will no longer be with us," Terry Tucker, the organization's chief strategy officer, told The Atlanta Journal Constitution. "He was a mentor for a lot of our residents. We look forward to finding an appropriate way to honour him here at City of Refuge."
Taos police found Scheib's vehicle June 16 at the Yerba Canyon trailhead. The 4-mile trail follows a canyon bottom before climbing to 3,700 feet in elevation, according to the U.S. Forest Service website.
As the search progressed, state police said they were exhausting all resources, from the New Mexico National Guard to the U.S. Air Force. High mountain peaks, deep canyons and dense vegetation made the air search difficult, while the rough terrain hampered efforts on the ground.