"Daddy, I love you and miss you so much. You were the best father anyone could ask for. Our relationship was so special, and you were always there for me. You gave me courage when I didn’t have any," she wrote in the caption of the song, which was posted on Chris Cornell's YouTube page.
Cornell recorded his own acoustic version of the song in 2015 and shared a studio version after Prince's death in April 2016.
Cornell died May 18, 2017, of an apparent suicide. Last year, Toni covered Leonard Cohen's "Hallelujah" on "Good Morning America" in tribute to her father and his longtime friend, Linkin Park's Chester Bennington.
Recently, Cornell's peers Pearl Jam paid tribute to the late singer during their performance at Ziggo Dome in Amsterdam on June 14. All members of the band wore Soundgarden shirts and other tees featuring Soundgarden's various alias to honor Cornell. Earlier in March, the dedicated a rendition of their song "Come Back" to the late singer.
Last month, Alice in Chains paid tribute to the singer by covering Soundgarden songs "Hunted Down" from 1991's Badmotorfinger and "Bootcamp" from 1996's Down the Upside.