Avri Borochov was born in Tel Aviv in 1981 into a working musical family. His father, the composer and arranger Yisrael Borochov, founded the East-West Ensemble, and his younger brother is the trumpeter Itamar Borochov, born in 1984. Borochov's training ran along two tracks at once. He studied classical double bass with Eli Magen of the Israel Philharmonic Orchestra, and at the same time worked on Indian rhythm with the tabla player Samir Chatterjee and on Afro-Brazilian percussion tradition with Mestre Camisa. He then moved to New York, took jazz instruction from Reggie Workman, Junior Mance, Peter Bernstein and Aaron Goldberg, and graduated from The New School in 2008 with a degree in jazz composition and performance.

He returned to Israel after that extended American period and has been based in Tel Aviv-Jaffa since. Since 2017 he has taught jazz double bass and directed ensembles at the Israeli Conservatory of Music in Tel Aviv, inside the jazz program the conservatory runs jointly with The New School, and he lists the New School faculty alongside it. He works as a mix engineer as well as a player, and both halves of that show up in his credits: he mixed the Guy Mintus Trio's Connecting the Dots (2019), a record with David Liebman on soprano saxophone, and he shares the mixing credit on the Uriel Herman Quartet's Face to Face from the same year, an album he also plays double bass and oud on.

His recorded career starts in Israeli small-label jazz. The earliest documented date is Naomi's Groove (2012) by the Mattan Klein Ensemble, where he holds the bass chair alongside Amos Hoffman and Ofer Ganor on guitars and Tom Oren on piano. In 2014 he played bass on his brother's debut, Outset, credited to the Itamar Borochov Quartet on RealBird Records with Hagai Amir on alto saxophone and Aviv Cohen on drums, and turned up in a very different setting the same year as a featured player on three tracks of the Tel Aviv producer Sol Monk's Beats, Not Words for Raw Tapes. He also played contrabass on tracks 3, 8 and 9 of Achinoam Nini's Love Medicine. Then came a dense 2016: bass, percussion and electronics as a core player on Shachar Elnatan's One World for Avishai Cohen's Razdaz Recordz label, with Gadi Lehavi on piano and Ofri Nehemya on drums; acoustic and electric bass on the flautist Avichai Ornoy's Sneakin' In for Jazz Family; bass on the drummer Yogev Shetrit's New Path; and the album that put him in front of an international audience, Boomerang.

Boomerang (Laborie Records LJ36, October 7, 2016) is the record where the brothers' band settles into shape. Borochov holds the double bass chair across the whole album, adds oud on "Ça va bien" and "Wanderer Song," and is credited with sazbush and voice on the latter, the track where their father guests on jumbush and voice. Track 7 is called "Avri's Tune." Two years later the same group made Blue Nights (Laborie Records LJ47), issued digitally on September 21, 2018 and on CD on February 4, 2019, with Rob Clearfield replacing Michael King at the piano and Jay Sawyer still on drums. Borochov plays bass throughout and doubles on oud on the title track, and The Jazz Mann's review singles out his solo on "Revolutionizin'" for its tone and melodic sense. The album took five-star reviews from DownBeat and UK Vibe. On his brother's fourth album, Arba (Greenleaf Music GRE-CD-1103, September 8, 2023), the working band had changed and Borochov appears only as a guest, playing oud on the third track.

His own line of work since has run through the pianist Uriel Herman's groups and through Israeli screen and stage music. He is a member of the Uriel Herman Quartet, playing double bass and oud on Face to Face (Laborie Records LJ55, January 25, 2019) and double bass on Different Eyes (Ubuntu Music UBU0136, June 30, 2023), the latter recorded at the Jerusalem Music Center with his brother on trumpet and Maayan Doari on percussion. He played double bass on the score Assaf Talmudi and Yonatan Albalak wrote for Gidi Dar's animated feature Legend of Destruction, which won the 2021 Ophir Award for Best Original Score, and he took the bass chair in Talmudi's trio at the 2026 Jerusalem Jazz Festival. At that same festival he appeared as a co-billed leader for the first time, in a new percussion-and-bass trio called "Pe'imot" with Maayan Doari and the Rio-born percussionist Jucca Perpiñán, built on Brazilian samba and candomblé, Spanish flamenco, and West and North African drumming.

Alongside the jazz work he is the arranger and musical director of two ensembles. Yamma, the Tel Aviv group led by the singer Talya G. A Solan that performs Hebrew and Jewish diaspora repertoire, has taken him to Roskilde in Denmark, Pohoda in Slovakia, Paléo in Switzerland, WOMAD, the Drammen Sacred Music Festival in Norway, Arts Midwest World Fest and the Rudolstadt Festival in Germany, where he was photographed on the bass in July 2023. The other is The Borochov Dynasty, the family band with his brother and their father, in which he plays double bass, oud and percussion and sings. His broader collaboration list, published on his own pages, runs from the jazz singer Kevin Mahogany, the Japanese guitarist Satoshi Inoue and the tabla player Samir Chatterjee to the flamenco singer Juan Pinilla and pianist David Dorantes, and inside Israel to Eli Degibri's big band, Daniel Zamir, the ECM pianist Anat Fort, the trumpeter Avishai Cohen, Omri Mor's trio at the 2010 Israel Festival, Berry Sakharof and Eviatar Banai.

Borochov's playing is built on a deliberately mixed foundation: an orchestral bassist's bow arm and sound from Eli Magen, a jazz vocabulary learned in New York from Reggie Workman, Junior Mance, Peter Bernstein and Aaron Goldberg, and rhythmic training in Indian and Afro-Brazilian traditions that most jazz bassists never touch. What makes him useful to a bandleader is that he covers two chairs at once, moving from the double bass to the oud inside a single record and sometimes a single tune, which is why Itamar Borochov's albums can carry maqam-inflected melody without a separate oud player on the payroll. Reviewers of that quartet single him out for a full, unhurried tone and for vamps that hold a groove rather than decorate it, and UK Vibe's notice of Blue Nights credits the bass and drums together with placing colour and texture where the music needs it. The Hebrew-language Israeli jazz press describes him as a boundary-crossing player, and his working life bears that out: a jazz teacher and jazz bassist by trade who spends as much time directing an ethno ensemble and mixing other people's records.