EXCLUSIVE

Alex Trebek has just been diagnosed with stage 4 pancreatic cancer, but not only will he finish out this season of "Jeopardy!" -- he has no plans to retire ... TMZ has learned.

Sources connected to Trebek tell us, the TV icon was just informed of the diagnosis. He recorded a video message announcing his diagnosis.

We're told Alex's will finish out the current season of "Jeopardy!." In fact, he says he's vowing to keep working and he's bravely upbeat. In the video, he says he plans to beat cancer.

Sources connected to the legendary host tell us he will immediately begin chemo.

Alex even managed to add some humor in his message, pointing out his contract calls for him to host for 3 more years -- and that's exactly what he intends to do.

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Former 'Jeopardy' champ Austin Rogers tells us he's confident "Mr. Trebek" will have tremendous support from his family, and adds ... his incredibly positive attitude will go a long way as he battles cancer.

Alex has been at the helm of the show since 1984 and it has been immensely successful ever since ... dominating the evening game show biz along with "Wheel of Fortune." Alex has always said he is not the star of the show ... he says it's all about the game and the contestants.

Trebek, who's from Ontario, Canada, got his start in 1961 announcing the news and other events on the Canadian Broadcasting Corporation. He quickly rose to prominence by hosting a live music show and eventually a high school quiz show, called "Reach for the Top."

Alex moved to the U.S. in 1973 and became the host of a new NBC show called "The Wizard of Odds" ... then worked on a variety of game shows until the early '80s before landing the "Jeopardy!" gig, which was actually a revival of an old show. It was a hit, and he's been doing it ever since ... often with his classic mustache. When he shaved his mustache off in the early 2000s, it made headlines.

Play video content JULY 2018 OBJECTIFIED

Last year, 78-year-old Alex spoke to Harvey Levin for an episode of "Objectified" and said he was seriously considering retiring, but he later signed a contract extension to secure his gig through the 2021-2022 season.

He does have a couple potential replacements in mind, though ... and he's pretty clear about it.