Cory Alexander Henry was born in Brooklyn on February 27, 1987. According to AllMusic he had picked up the organ and the piano by the age of two from his mother, Marie, a choir director and multi-instrumentalist. At five he was known around church as "Master Henry" for his ability to accompany any song in any key on the Hammond B3, and at six he made his debut at the Apollo Theater. By high school he was a name on the New York scene through his performances at the Village Underground.

At 19 he was hired by the saxophonist Kenny Garrett and stayed in that touring band for about three years, an apprenticeship that led to work with a wide range of artists. He has toured or recorded with the gospel stars Yolanda Adams, Israel Houghton, Kirk Franklin and Donnie McClurkin, and with Bruce Springsteen, Michael McDonald, Boyz II Men and The Roots. He released early albums of his own, a holiday set called Christmas with You and then Leave You Alone, before Michael League asked him in late 2011 to join Snarky Puppy. His first recorded appearance with the band was groundUP (2012); the same year he issued Gotcha Now Doc under the name Cory Henry M.D. His solo album First Steps (Wild Willis Jones, July 21, 2014) reached No. 5 on the Billboard Top Jazz Albums chart and No. 30 on the Heatseekers chart.

Henry's years in Snarky Puppy overlap with the band's run of Grammy wins. He is credited on piano and keyboards on Family Dinner - Volume 1 (2013), whose "Something," sung by Lalah Hathaway, won the Grammy for Best R&B Performance on January 26, 2014. On We Like It Here (2014), recorded live in Utrecht, he took a well-regarded synthesizer solo on "Lingus." On Sylva (2015), recorded with the Metropole Orkest in Dordrecht, he played Hammond B3, Moog and clavinet, and the album won the Grammy for Best Contemporary Instrumental Album in 2016. Culcha Vulcha (2016), on which he is credited with clavinet, organ, Mellotron, Omni, Moog and piano, took the same award in 2017. His own live album The Revival (GroundUP / Universal, March 18, 2016), recorded and filmed at the Greater Temple of Praise in Brooklyn, reached No. 5 on the Top Gospel Albums chart and No. 2 on the Top Jazz Albums chart. In the same years he took the organ solo on the third track of Marcus Miller's Blue Note album Afrodeezia (2015) and played organ on two tracks of David Crosby's Lighthouse (2016).

In 2018 he left Snarky Puppy, moved to California and started a solo career fronting his band, the Funk Apostles. The single "Trade It All" came out on April 13, 2018, and the album Art of Love followed on July 13, with a digital-only live recording from Los Angeles after it. In 2019 Quincy Jones chose him to headline a night of his Soundtrack of America series at the opening of The Shed in New York. Something to Say, recorded in 2019 and released on October 30, 2020, was nominated for the Grammy for Best Progressive R&B Album at the 64th Grammy Awards. Best of Me (September 17, 2021) put him up front as a singer, playing Hammond B3, Moog and the Harpejji on songs inspired by Stevie Wonder, Marvin Gaye, Donny Hathaway, Parliament-Funkadelic and James Brown.

His session and production work in this period reached well beyond jazz. He played organ on "24" from Kanye West's Donda (2021), also known as "Run to Glory," and is credited as co-producer and co-writer; Beats used the track in a commercial on August 5, 2021, and Donda was nominated for Album of the Year and Best Rap Album. He played organ on "G3 N15" from Rosalía's Motomami (2022), which won the Grammy for Best Latin Rock or Alternative Album, and is credited on records by Imagine Dragons, Red Hot Chili Peppers, Robert Randolph, Ledisi and Billy Strings. Operation Funk (2022) was nominated for Best Progressive R&B Album, and a live version released the same summer featured Kamasi Washington on saxophone and the guitarist Eric Gales. In September 2022 he announced that he planned to step back from the music business.

That plan did not last. Live at the Piano (May 24, 2023), a set of his own compositions, was nominated for Best Alternative Jazz Album at the 66th Grammy Awards. Church (February 25, 2024), a 23-track gospel revue with recordings of his mother and his grandmother, Dr. Janice McDonald, alongside Kierra Sheard, Raphael Saadiq, Robert Randolph, Kim Burrell, Donnie McClurkin and John P. Kee, won the Grammy for Best Roots Gospel Album at the 67th Grammy Awards in February 2025, his first win under his own name. In 2024 he joined Stevie Wonder's band for the Sing Your Song! tour and wrote and recorded the six-song A Wonderful Holiday in studios between arena dates; it was released in late 2025. He has also released Divine Time (August 22, 2025) and the EP We're Having Good Church (June 24, 2026). His newest album, Devotion (Apostle Music Group, August 27, 2026), has ten songs with guests including the gospel artists Fred Hammond and Hezekiah Walker, and a harmonica solo by Stevie Wonder on "Something Happens." At 39 he continues to tour with the Funk Apostles.

Henry is first a Hammond B3 player, and the instrument ties together everything he does. AllMusic describes his approach to the B3 and the piano as heavily influenced by Art Tatum and Oscar Peterson, combining gospel, blues and jazz, and calls him one of the finest B3 players of his generation, in a line that runs through Jimmy Smith and Billy Preston. As a singer and bandleader he draws on Stevie Wonder, Marvin Gaye, Donny Hathaway, Parliament-Funkadelic and James Brown.

The jazz side of his career is documented: a three-year apprenticeship in Kenny Garrett's band, six years in Snarky Puppy (whose Grammy-winning albums are instrumental fusion and funk), organ and keyboard credits for Marcus Miller, Robert Glasper, Gary Bartz, Terrace Martin, Boney James and Me'Shell Ndegéocello, Top Jazz Albums placements of No. 5 and No. 2, and a Best Alternative Jazz Album nomination for Live at the Piano. The rest of his own catalog sits outside jazz and should be heard that way: Church and Devotion are gospel records, and Something to Say, Best of Me and Operation Funk are R&B, soul and funk albums, two of them nominated in the Progressive R&B category. He is as much a church musician and funk bandleader as a jazz organist, and his Grammy history reflects it: one win and five nominations across gospel, R&B, jazz and the Donda album.