Born on October 27, 1954, Brunious was born into a Louisiana Creole family, the son of Nazimova “Chinee” Santiago and John “Picket” Brunious, Sr., a trumpeter who studied at Juilliard and played with the Onward Brass Band, Young Tuxedo Brass Band, and Paul Barbarin, and who arranged for Billy Eckstine and Cab Calloway. Brunious’ brother John Brunious, Jr. was another notable New Orleans jazz trumpeter and a predecessor as bandleader of Preservation Hall Jazz Band. His nephew is Mark Braud, a successor as bandleader of Preservation Hall Jazz Band.
Brunious sang in Chief John and the Mahogany Hall Stompers in the 1960s, a group in which his father was also a member. He began on trumpet at age 11 and played at Paul Barbarin’s funeral. He studied at Southern University (where he played with Danny Barker) and played dance music in clubs on Bourbon Street in the middle of the 1970s.
In 1976, Brunious substituted for his father in Albert “Papa” French‘s band for Mardi Gras, and by 1979 was playing regularly at Preservation Hall with Kid Thomas Valentine. He was named leader of the group upon Valentine’s death in 1987. He also played with the Eureka Brass Band (1980), Lionel Hampton(1981), Linda Hopkins (1984), and Sammy Rimington (1984). He played with Louis Nelson in 1986-89, and did recordings with the Caledonia Jazz Band of Norway in 1986 and 1987. His first record as a leader came in 1986, which featured Nelson, Rimington, and Barry Martyn as sidemen. He later played with Dr. Michael White, Chris Barber, Papa Don Vappie, Bob Wilber and the Pfister Sisters. He remained a regular performer at Preservation Hall into the 2000s.
Wendell Brunious married Rita (Hoard) Brunious in New Orleans in 1984. They have two children, Meredith Brunious, a New Orleans costumer and Brandon Brunious, a New Orleans jazz bassist and guitarist. The couple divorced in 2004, after which Brunious lived in Sweden from 2004 to 2011 with clarinetist Caroline Fromell and their sons Jonathan and Matthew.  Brunious currently resides and plays regularly in New Orleans, Louisiana.