A family source tells TMZ the Welsh musician died peacefully Monday in a California hospital of heart failure after a battle with pneumonia. Davis had an extraordinary career that spanned 6 decades ... and the source emphasized how much he'll be missed by his friends, family and loved ones.

Davis formed the British group bearing his name in 1963, which featured himself on guitar and Pete York on drums ... and he recruited a teenage Steve Winwood to sing and Steve's brother, Muff, to play the bass.

It didn't take long for the band to break out with a #1 single -- "Keep on Running" -- in 1965 ... followed by another hit, "Somebody Help Me," in 1966.

The following year, The Spencer Davis Group released their most famous track -- "Gimme Some Lovin'" -- which was a top 10 hit ... and "I'm a Man." Both singles sold over a million copies and achieved gold record status.

Though the band broke up in 1969 after just 6 years together, their music had a huge influence on the sound of the era.

Davis embarked on a solo career afterward, but was never able to reach the success of his group. He also served as an exec for Island Records in the '70s.

Davis is survived by his 3 children -- Lisa, Sarah and Gareth -- and 5 grandchildren.

Spencer was 81.