The US singer-songwriter credited his late wife, who died peacefully at their home on Tuesday, as being the "emotional security" he needed to have a career in the music industry.
The couple's relationship inspired a biopic in 2014 titled Love & Mercy starring John Cusack and Paul Dano as Brian, which follows him under the sway of a controlling therapist, before finding his "saviour" Melinda, played by Elizabeth Banks.
Sharing a series of pictures on Instagram, Wilson said: "Melinda, my beloved wife of 28 years, passed away this morning. Our five children and I are just in tears. We are lost.
"Melinda was more than my wife. She was my saviour. She gave me the emotional security I needed to have a career.
"She encouraged me to make the music that was closest to my heart. She was my anchor. She was everything for us."
A statement from their five children described their late mother as a "force of nature" and "one of the strongest women you could come by".
"She was not only a model, our fathers saviour, and a mother, she was a woman empowered by her spirit with a mission to better everyone she touched," the statement said.
"We will miss her but cherish everything she has taught us. How to take care of the person next to you without expecting anything in return, how to find beauty in the darkest of places, and how to live life as your truest self with honesty and pride."
Among those sending their condolences was US actor Alec Baldwin, ahead of his arraignment on a charge of involuntary manslaughter over the fatal shooting on the film set of Rust.
He said: "So sorry."
Meanwhile musician Graham Nash said: "I'm deeply sorry for your loss, Brian, and for the terrible hurt you are all feeling. My heart, love, and prayers are with you and your family."
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