2:06 PM PT -- Suzanne's rep tells us ... "Her family was gathered to celebrate her 77th birthday on October 16th. Instead, they will celebrate her extraordinary life, and want to thank her millions of fans and followers who loved her dearly. A private family burial will take place this week, with a memorial to follow next month."

Sources close to the late actress also tell us that Suzanne had recently been seeking treatment for her breast cancer out of state in the Midwest -- but we're told it proved to be unsuccessful and she was ultimately brought home.

Suzanne Somers has died after a long battle with cancer ... this according to her team.

The legendary actress -- famous from "Three's Company" and a score of other TV shows/movies -- passed away Sunday morning at her home ... so says her publicist, R. Couri Hay, who broke the tragic news to Page Six.

He says, "Suzanne Somers passed away peacefully at home in the early morning hours of October 15th. She survived an aggressive form of breast cancer for over 23 years. Suzanne was surrounded by her loving husband Alan, her son Bruce, and her immediate family."

It's a heartbreaking development for the showbiz icon ... who's been dealing with cancer, in one form or another, since the early 2000s. She was first diagnosed with melanoma in 2000 ... and developed breast cancer shortly thereafter. SS battled breast cancer on and off for years ... but it fully returned just earlier this year in the summer, when she told the world.

At the time, she wrote ... "As you know, I had breast cancer two decades ago, and every now and then it pops up again, and I continue to bat it down. I have used the best alternative and conventional treatments to combat it. This is not new territory for me. I know how to put on my battle gear and I’m a fighter."

Obviously, she'll best be remembered for her work on the famed ABC sitcom opposite John Ritter and Joyce DeWitt -- where she played the hilarious and ditzy Chrissy Snow for five seasons -- but her work spanned decades ... and was notable well beyond that.

Suzanne is also well-known for roles in "Starsky and Hutch," "Hollywood Wives," "She's the Sheriff," "Step by Step," and countless one-time appearances on several other hit series.

Movie-wise, her work on "American Graffiti" is her biggest claim to fame on the big screen -- but Suzanne starred in a number of films ... including "Ants!" "Yesterday's Hero," "Nothing Personal," "Serial Mom," "The Nutty Professor," "Say It Isn't So" and more. She hasn't acted since 2001, right around the time her health troubles surfaced.

Suzanne's death comes just one day before her 77th birthday. She's survived by her son, Bruce Jr.

She was 76.

RIP