The song and its accompanying video, in which the "Ironic" singer and her family recreate their own bed-in - mirroring Lennon and Ono's, dropped on Friday, November 27.
The promo also features classic family home videos of Christmases past and footage of Morissette's bandmates celebrating the holidays with their families. The video further offered a look at her cuddling up with her husband Souleye and their children, Onyx, Ever and Winter.
"It is an honour to cover this heartwarming song," Alanis says. "The lyrics feel more pertinent than ever and this year has been a year of great resilience and adapting and feeling all the feelings. May this song serve as a big hug to you and your sweet families and friends. Everything is going to be OK in the end, and if it's not OK, it's not the end."
Fans were totally in love with the cover. "A very big thank you @Alanis for this fun updated John Lennon classic. War is Over," one fan wrote on Twitter.
Alanis, who released her ninth studio album, "Such Pretty Forks in the Road", in July, will also perform on the Tina Fey-hosted "One Night Only: The Best of Broadway" special on NBC next week (December 4). The event will benefit Broadway Cares/Equity Fights AIDS, a nonprofit that supports the Actors Fund.