In 1980 Ignacio left his country during the Mariel Boatlift, moved to New York and joined Dizzy Gillespie’s quartet. in 1981, becoming the drummer of all the important band Gillespie formed until his death in 1993.

His first album as a leader, Codes, released under Blue Note Records, was nominated for a Grammy in 2006. Codes also won a Danish Music Award in 2007 as best International Jazz Album. He was honored by inclusion in the 2011 Blue Note and Modern Drummer Release titled "Jazz Drumming Legends". His album Heritage and Passion was recorded on 2014.

Ignacio has recorded and played with musicians of the stature of McCoy Tyner, Chick Corea, Wynton Marsalis, Freddie Hubbard, Jackie McLean, Michael Brecker, Milt Jackson, Jaco Pastorius, Ron Carter, Charlie Haden, Tito Puente, Mario Bauzá, Gonzalo Rubalcaba, Gilberto Gil, Ivan Lins, Joao Bosco, Lenny Andrade, and Lincoln Center Orchestra, WDR Big Band and BBC Big Band just to name a few.

Featuring Bill Cunliffe, piano, Bob Sheppard, saxophone, and Chris Colangelo, bass.