Born in Israel, Yavnai began playing piano at the age of four. He has professionally accompanied singers since the age of thirteen. He graduated from the Thelma Yalin High School for Arts and subsequently the Givatayim Conservatory, both in Israel. Alon later furthered his studies at the Berklee School of Music in Boston, Massachusetts and soon after took first place in the Great American Jazz Piano Competition.
Alon is a favorite artist of Grammy-winning saxophonist and clarinetist Paquito D'Rivera. Their collaborations include the Alon Yavnai-Paquito D'Rivera Duet, the Jazz Chamber Trio with Turtle Island String Quartet cellist Mark Summer, and the Latin Jazz Quintet. Alon also accompanies violinist Regina Carter, the New York Voices, and leads his own Alon Yavnai Trio. He has also performed with musicians such as Freddie Hubbard, Joe Lovano, Nancy Wilson, Rosa Passos, Leni Andrade, Louis Hayes, Bob Moses, Ravi Coltrane, Romero Lubambo, Claudio Roditi, Rufus Reid, Jim Chapin, and George Garzone.
He has taught, being a former faculty member at the Sitka Fine Arts Camp.
In 2008, Yavnai won a Grammy as a part of the Paquito D'Rivera Quintet for Best Latin Jazz Album for Funk Tango. Yavnai wrote the title track. In May 2008, Yavnai released his album Travel Notes which features solo pieces as well as trio pieces (with Omer Avital on bass and Jamey Haddad on percussion).
- Travel Notes, ObliqSound (2008) w/ Omer Avital-b, Jamey Haddad-perc
- Picture This, Bon Rapport Music (2004) w/ Massimo Biolcati-b, Take Toriyama-d and special guest Paquito D'Rivera-s
- D.S. Al Coda, Whaling City Sound (2001) w/ George Garzone-s, Dino Govoni-s/f, Avishai Cohen-tr, Massimo Biolcati-b, Take Toriyama-d, Michael Cohen-v, Baoz Nemet-darbouka
- Paquito D'Rivera: Funk Tango, Sunnyside Records/Paquito Records (2007)
- Nancy Wilson: Turned to Blue, MCG Jazz (2006)
- Caribbean Jazz Project/Dave Samuels: Mosaic, Concord Picante (2006)
- Gregg August: Late August, Iacuessa Records (2005)
- Paquito D'Rivera: Jazz Chamber Trio, Chesky Records (2005)