The US star rose to fame with the power pop group the Raspberries before establishing himself as a solo artist.
Hungry Eyes, one of his huge solo hits, featured in 1987 cult movie classic Dirty Dancing.
"Our sweet, loving and talented Eric passed away in his sleep, over the weekend," Carmen's wife Amy said in a statement on his official website.
"It brought him great joy to know, that for decades, his music touched so many and will be his lasting legacy."
She ended the statement with the quote "love is all that matters... faithful and forever" from his 1977 solo album Boats Against The Current.
The Ohio-born singer co-founded the Raspberries in the early 1970s alongside Jim Bonfanti and Wally Bryson, who were later joined by Dave Smalley after the departure of John Aleksic.
They released their debut album Raspberries in 1972, with tracks reaching chart success including Go All The Way - which was later banned by the BBC in the UK for sexually suggestive lyrics and was later included on the 2014 Guardians Of The Galaxy soundtrack.
After four albums together, the band broke up in 1975 with Carmen then embarking on a solo career.
Among the solo tracks he is most well-known for is All By Myself, which later became one of Canadian singer Celine Dion's most iconic hits when she covered it.
The song also featured in the opening scene of Bridget Jones's Diary.
As a songwriter, Carmen had hits including Almost Paradise from the Footloose soundtrack, as well as Never Gonna Fall In Love Again and Make Me Lose Control.
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