The Iceland international had two spells in Scotland, first with Celtic from 1975 to 1980 where he twice won the Scottish League Championship then with The Steelmen from 1982 to 1984.
A statement on the Motherwell FC website read: “We are saddened to learn of the news of the death of Johannes Edvaldsson at the age of 70.
"The former Iceland international played for Motherwell between 1982 and 1984, arriving from German side Hannover 96.
"An uncompromising defender, ‘Shuggie’, as he was known, made 65 appearances in claret and amber, netting six goals. Primarily playing at the back, he could also be deployed to great effect further up the pitch.
"Everyone at Motherwell FC’s thoughts are with his family.”
A statement on the Celtic FC website read: “Everyone at Celtic is saddened to hear of the passing of former player, Johannes Edvaldsson, who has died at the age of 70.
"Johannes, or ‘Shuggy’ as he was affectionately known by Celtic supporters, was an Icelandic internationalist who joined Celtic in 1975 following a short trial with the club. He went on to make 195 appearances for the club over the next five years, scoring 38 goals.
"He won two league titles and one Scottish Cup with Celtic – the league and cup double in 1977 and, most famously, playing his part in the 1979 title triumph, when the Hoops beat Rangers 4-2 at Paradise to become champions, an event that has gone done in Celtic folklore as the night 10 men won the league.
"Johannes left the club in 1980 to joined Tulsa Roughnecks in the United States, but returned to Scotland two years later, and played for two seasons with Motherwell.
"The thoughts and prayers of everyone at Celtic are with Johannes’ family at this very sad time.”
Celtic have also confirmed they will hold a minutes silence for Edvaldsson ahead of their match tomorrow night at Parkhead with Hamilton Accies.
The thoughts of everyone at the Motherwell Times are also with Edvaldsson's family at this sad time.