The US pop trio enjoyed hits like The Sun Ain’t Gonna Shine Anymore and Make It Easy On Yourself in the 1960s.
The band moved to Britain and at one point their fame in their adopted country rivalled that of The Beatles.
Record label 4AD said: “It is with great sadness that we announce the death of Scott Walker.
“Scott was 76 years old and is survived by his daughter, Lee, his granddaughter, Emmi-Lee, and his partner, Beverly.
“For half a century, the genius of the man born Noel Scott Engel has enriched the lives of thousands, first as one third of The Walker Brothers, and later as a solo artist, producer and composer of uncompromising originality.
“Scott Walker has been a unique and challenging titan at the forefront of British music, audacious and questioning, he has produced works that dare to explore human vulnerability and the godless darkness encircling it.”
Walker, who was born in the US, began his career as a session bassist, changing his name when he joined The Walker Brothers.
He later shunned the limelight and released solo albums including Scott, Scott 2, Scott 3 and Scott 4.
In the 1970s The Walker Brothers reunited for their last album together.
In 2017, Scott’s music was celebrated with a Proms concert at London’s Royal Albert Hall.
The record label said the singer “has been one of the most revered innovators at the sharp end of creative music”.
Radiohead frontman Thom Yorke said he is “so very sad” to hear of the death of Walker, whom he said was a “huge influence” on himself and his band.
He tweeted: “So very sad to hear that Scott Walker has passed away, he was a huge influence on Radiohead and myself, showing me how I could use my voice and words.
“Met him once at Meltdown, such a kind gentle outsider.
“He will be very missed.”