The cancellations were ordered by Riverside County's public health officer.
Dr. Cameron Kaiser said he signed the order out of concerns about a second wave of coronavirus in the fall.
"I am concerned as indications grow that COVID-19 could worsen in the fall," said Kaiser. "In addition, events like Coachella and Stagecoach would fall under Governor Newsom's Stage 4, which he has previously stated would require treatments or a vaccine to enter. Given the projected circumstances and potential, I would not be comfortable moving forward.
"These decisions are not taken lightly with the knowledge that many people will be impacted. My first priority is the health of the community."
Earlier this year as the coronavirus pandemic was growing, organizers of both events announced they had been rescheduled for October.
Then last week, Coachella organizers starting reaching out to performers asking them to play in 2021 instead of October, according to Bloomberg News.
Some 250,000 people attend the Coachella Valley Music and Arts Festival's two weekends in Indio every year in April.
COVID impact: One of America's first 'socially distant' concert gives glimpse into future of live events