He was 56.
Mould, 56, penned a hearfelt anecdotal note on Facebook to his band member, with whom he spent nine years of his life creating "amazing music together".
"It was the Fall of 1978. I was attending Macalester College in St Paul, Minnesota. One block from my dormitory was a tiny store called Cheapo Records. There was a PA system set up near the front door blaring punk rock.
"I went inside and ended up hanging out with the only person in the shop. His name was Grant Hart," he wrote, alongside their black-and-white photograph.
He called him "a gifted visual artist, a wonderful story teller and a frighteningly talented musician".
"Everyone touched by his spirit will always remember. Godspeed, Grant. I miss you. Be with the angels," he wrote.
Mould said the news of Hart's passing was not unexpected to him and offered condolences to his family, friends and fans around the world.
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