The Light Medium Tactical Vehicle (LMTV) overturned where Route 293 connects with the Camp Natural Bridge training site around 6:45 a.m.
The cadets, all rising seniors at West Point, were involved in what military officials described as a standard training exercise just a few miles away from the academy at the time of the crash.
One cadet was confirmed dead at 10:58 a.m., while 19 other cadets and two active-duty soldiers who were operating the vehicle were injured.
WATCH: Official briefing on deadly West Point crash
They were taken to Keller Army Community Hospital and other regional medical facilities with a variety of injuries described as not life threatening.
The names of all the personnel involved were being withheld pending notification of family members.
One cadet is reported deceased, 20 cadets and two soldiers are wounded that were involved in a Light Medium Tactical Vehicle accident that occurred at approximately 6:45 a.m. off Route 293.— U.S. Military Academy (@WestPoint_USMA) June 6, 2019
Route 293 was closed for a short time but has since reopened.
"My heart breaks for all those involved in the tragic training accident at West Point this morning," Governor Andrew Cuomo said in a statement. "These courageous cadets and soldiers represent the best of New York State and our country, and we owe them a debt of gratitude for their bravery in choosing to serve our country and protect our freedoms. This incident is made all the more heart wrenching as we commemorate the 75th anniversary of D-Day today, a day where we remember those who gave their lives for our country. I am grateful to the first responders who are on the scene right now and am directing the State Office of Emergency Management to provide any resources necessary to assist. On behalf of all New Yorkers, we pray for a speedy recovery for those involved and we share in the sorrow experienced by their loved ones during this extremely difficult time."
President Donald Trump also tweeted about the incident.
So sorry to hear about the terrible accident involving our GREAT West Point Cadets. We mourn the loss of life and pray for the injured. God Bless them ALL!— Donald J. Trump (@realDonaldTrump) June 6, 2019
Classes ended at West Point last month, but the academy runs summer military training exercises in the heavily wooded hills outside the main gates.
The rollover occurred on a fire break road as the vehicle was leaving Camp Natural Bridge, where about 2,400 trainees live during the summer.
They were en route to Land Navigation Training, part of regular training for West Point cadets. The terrain where the crash occurred was described by military officials as rugged and hilly, which is common in that region.
The investigation of the cause of the single-vehicle accident was continuing.
West Point is on the Hudson River about 50 miles north of New York City.