Dunn, an integral part of the Memphis soul sound as bassist for the MGs, the house band for Stax and Volt records, died on Sunday after finishing two shows at the Blue Note Night Club in Tokyo, Cropper said in a posting on his Facebook page.
"Today I lost my best friend, the world has lost the best guy and bass player to ever live," Cropper said.
Cropper, who also performed with Dunn on television and in the movies as part of the MGs-inspired Blues Brothers tribute band, said Dunn had died in his sleep, but he gave no other details about the circumstances.
The signature instrumental grooves of Booker T. & the MGs, grounded by Dunn's heavy bass notes, provided the musical bedrock on hundreds of singles for such soul stars as Wilson Pickett, Otis Redding, Eddie Floyd and Sam & Dave.
From Redding's wistful "(Sittin' On) The Dock of the Bay" to Picket's raucous "In the Midnight Hour," the band's lean, tight accompaniment carried the vocals.
The group, inducted into the Rock and Roll Hall of Fame in 1992, also cut 10 albums and charted 14 hits of their own, including "Hip Hug-Her," "Groovin'," "Soul-Limbo," "Hang 'em High" and "Time Is Right."
The first and biggest instrumental hit of the MGs (an abbreviation for "Memphis Group") was recorded in 1962 before Dunn joined - "Green Onions," a 12-bar blues composition that has become a staple for aspiring rockers ever since.
Their most notable collaboration was with Redding, Stax's greatest star. The group played on virtually all of his records and backed him l i ve for his legendary performance at the Monterey Pop Festival in 1967.
Cropper co-wrote Redding's most popular hit, "(Sittin' On) The Dock of the Bay," and shared songwriting credits on such soul standards as Pickett's "In the Midnight Hour" and Floyd's "Knock On Wood."
Dunn also played in sessions for many artists outside the realm of soul, including Eric Clapton, Neil Young and Jerry Lee Lewis.
In contrast to the more orchestrated pop-soul sound of Detroit-based Motown Records, the soul stylings produced by the Stax/Volt labels in Memphis were defined by the MGs' spare, punchy and deeply groove-laden instrumentals.
The group, formed in the early 1960s, originally consisted of its namesake organist, Booker T. Jones, guitarist Cropper, drummer Al Jackson and bassist Lewis Steinberg. But the definitive lineup of the MGs was completed after a couple of years when Steinberg was permanently replaced by Dunn, who had started out with Cropper in a band called the Mar-Keys.
The MGs gradually broke up after Stax was sold in 1968, although the rhythm section of Dunn and Jackson continued to play on many subsequent Stax recordings. Jackson was shot to death in his Memphis home in 1975 as the group was preparing a reunion album.
In the 1990s, the surviving members reunited to back Neil Young on a tour and released "That's the Way It Should Be," their first album in more than 20 years.
Dunn and Cropper also performed in the Blues Brothers Band, a group originally assembled to back John Belushi and Dan Aykroyd for a 1978 comedy sketch on "Saturday Night Live." They also appeared together in the 1980 "Blues Brothers" movie and its 1998 sequel, "Blues Brothers 2000."