TMZ has reported that Alex Trebek -- the revered and beloved "Jeopardy!" host since 1984, whose calm but witty presence was must-see television for millions of Americans -- has died ...

A "Jeopardy!" spokesperson tells TMZ, "Jeopardy is saddened to share that Alex Trebek passed away peacefully at home early this morning, surrounded by family and friends."

The TV icon had been battling stage 4 pancreatic cancer since announcing the news back in March 2019. He immediately started chemo after the diagnosis, but made no plans to retire and continued hosting his game show ... as impressively as ever