Anthony was born Marco Antonio Muñiz in New York of Puerto Rican parents who named him after a Mexican singer. He began his career as a session vocalist for pop and dance acts.
After changing his name, Anthony worked as a songwriter and backing vocalist for pop acts including Menudo and the Latin Rascals. He subsequently collaborated with producer Little Louie Vega, who featured the singer on the Latin-flavored club hit "Ride On The Rhythm" and When The Night Is Over. In 1992, Vega and Anthony opened for Latin bandleader Tito Puente at New York's Madison Square Garden.
Inspired by the music of Puente, Rubén Blades and Juan Gabriel, Anthony released his Spanish-language debut, Otra Nota, in 1993, with the hit "Vivir Lo Nuestro", a duet with singer La India. Subsequent tours throughout the Americas, including an opening slot for Blades, established Anthony as one of the hottest new stars in salsa.
His 1995 collection, Todo A Su Tiempo, was nominated for a Grammy. The more traditional-sounding follow-up, Contra La Corriente, was promoted by a sell-out concert at Madison Square Garden and won the 1999 Grammy for Best Tropical Latin Performance. Anthony also appeared alongside Blades in Paul Simon's 1998 stage musical, The Capeman, which ran for 68 performances. Anthony subsequently recorded the duet "No Me Ames", with Jennifer Lopez on her The 6 collection.
In 1999, attempting to emulate the crossover success of Jennifer Lopez and Ricky Martin in the anglophone market, Anthony released an English-language album with the US Top 5 hit single "I Need To Know". The foray was considered a mixed success, partly because it alienated his traditional salsa fans.