Shannon was born in Tucson, Arizona, and moved to the Texas Panhandle when he was nine. He grew up mainly in Dumas, Texas, north of Amarillo on Highway 287. Shannon joined his first band, The Avengers, around age 13. The band members were Shannon (guitar), Tim Easley (vocals), Jim Love (guitar) and David Davis (drums). It would be a while before they realized the importance of the bass guitar, but eventually Shannon did. Their first gig paid them $80. That excited them so much, they gave half their paycheck back.
In high school Shannon was in the band Ekos. Soon after high school he moved to Dallas and joined a soul cover band in 1966, initially called The New Breed, and later The Young Lads. Shannon recorded two 45s with this band, which featured Tim Easly on vocals and Uncle John Turner on drums.
Shannon had the first of two important meetings at The Fog in Dallas in the late 1960s. There he first saw Johnny Winter. Shannon ended up backing Winter, and they formed a project known as The Progressive Blues Experiment in 1968. They cut one album for Sonobeat Records titled The Progressive Blues Experiment before being signed to Columbia Records by Clive Davis for $600,000 in 1969. Shannon appeared on both of these Columbia LP's, each released 1969; Johnny Winter (self-titled), and Second Winter. At Woodstock, Johnny's brother Edgar joined them onstage. Johnny Winter ended up moving to a band featuring Rick Derringer in early 1970 that already had a rhythm section, and there was no room for Shannon or Turner. They landed in a San Francisco band called Krakerjack that comprised Uncle John Turner, drums; Mike Kindred, piano; Shannon, bass; Bruce Bowland, vocals; and John Stahely, guitar, Jesse "guitar" Taylor played lead guitar with the band as well for a time during 1970 (there is a band photo as proof). According to Tommy's website, Stevie Ray Vaughan, known as "Skeeter," was part of this band in its later Austin incarnation, along with Robin Syler on guitar. Krakerjack apparently remained a group from 1970 to 1971.
During the 1970s, Shannon became involved with drugs, and began a cycle of jail, probation and rehab that would last for some time. He played with the Austin band The Fools briefly. Due to recurring drug arrests and failure of rehab in San Antonio and other locations, Shannon was finally sent to a "farm" in Buda and, as a result of his probation on release, he was not allowed join any bands because of the pervasiveness of drugs in the music scene. Shannon became a bricklayer for a few years until he was eventually able to return to music in 1977. He played in a few unknown bands, then received a call from Rocky Hill, brother of ZZ Top's Dusty Hill. He moved to Houston to play with Hill and Uncle John, and in the late 1970s went on to play with Alan Haynes in the "Texas Boogie Band" (Shannon later played on Haynes' well received 1994 release, "Wishing Well"). Shannon also toured, opening for Bachman–Turner Overdrive and for KISS at the Warehouse in New Orleans.
Shannon moved between Dallas and Austin, and saw Stevie Ray Vaughan at The Fog with Vaughan's group Blackbird. Vaughan later formed a group called Double Trouble, and in 1980 Shannon wound up taking the place of the bass player, Jackie Newhouse, after seeing Double Trouble at Rockefellers in Houston. The group could have been short-lived—Vaughan was tapped to do some guitar tracks for David Bowie (the haunting guitar on "Let's Dance", for instance), and was then offered the chance to tour with Bowie. Ultimately, Vaughan's manager turned down the offer. Vaughan, Shannon and drummer Chris Layton would stay together as Stevie Ray Vaughan & Double Trouble—and become one of the most famous blues bands of all time.
After joining Double Trouble, Shannon met his future wife Kumi and they eventually married in 1986. He had returned to ever-increasing drug use, this time with the band leader. Eventually both realized that they wouldn't last if that lifestyle continued, so they checked into rehabilitation in separate cities and both became clean and sober. Things seemed like they couldn't be better, with the band being healthier, making popular music, and gaining fame and fortune—until the helicopter carrying Vaughan crashed into a hillside after a show at Alpine Valley Music Theater, near East Troy, Wisconsin, on August 27, 1990, and all aboard died.
After a period of mourning, Shannon's musical career eventually continued. He played with Doyle Bramhall, Denny Freeman and Chris Layton in The Mighty Zor. Shannon was asked by The Rolling Stones to audition to replace Bill Wyman, but did not get the role. Other notable projects included the Arc Angels with Doyle Bramhall II and Charlie Sexton, and Storyville with Malford Milligan. He toured with Susan Tedeschi and, along with Chris Layton, toured and recorded with Kenny Wayne Shepherd. He and Layton played on Jimmy D. Lane's "It's Time". He has played with other notable musicians, including Eric Clapton, The Rolling Stones, Little Richard, Hubert Sumlin, Mike McCready, Jonny Lang, Buddy Guy, Jimmie Vaughan, Eric Johnson, David Grissom, Mato Nanji, Jeff Beck, Lou Gramm and John Mayer.
In 2001, Double Trouble reformed, releasing their only album without Vaughan. Titled "Been a Long Time", it featured many guest performers (including Tedeschi) filling Vaughan's frontman role.
His primary bass was a battered Arctic White 1962 Fender Jazz Bass with a red tortoise shell pickguard. He has been seen playing Yamaha BB's, Music Man StingRays, other Fender Precision and Jazz basses (mostly American, American Deluxe and Custom Shop models) and custom Fodera basses.
Shannon was inducted into the Rock and Roll Hall of Fame as a member of Double Trouble in 2015.