The former reality star is one of several celebrity contestants on the new series of the US version of Strictly Come Dancing, which began in the US last night.
Jack is paired with pro dancer Cheryl Burke, who has won the show twice.
Last night, the couple got off to a flying start with their foxtrot, earning 23 out of 30 points from judges Len Goodman, Bruno Tonioli and Carrie Ann Inaba.
Proud parents Sharon and Ozzy, and wife Lisa, watched from the audience. His sister Kelly, who has appeared as a contestant on the show in the past, wasn't able to attend as she's in the UK.
Kelly tweeted last night: "In London almost 1am I can't sleep all I am thinking about is my brother @JackOsbourne I cant stand that Im not there to support him #dwts."
But Jack had plenty of support from his parents. Sharon tweeted: "@OfficialOzzy and I are SO PROUD of @JackOsbourne! He's never danced before & he just did fabulous on @DancingABC!"
Sharon was in tears as she watched Jack's performance, which came following the heartbreaking news that wife Lisa had suffered a miscarriage while pregnant with their second child.
Jack also has multiple sclerosis and has said he's doing the show to raise awareness of the condition.
"There is this huge stigma around multiple sclerosis that once you're diagnosed you're a disabled person who can't do anything and you're cast out of society and that's just not the case," he said. "Right now I'm physically able to do DWTS but it might not always be that way so I don't want to miss this opportunity."
Other stars competing on DWTS this year include Snooki, Saved By The Bell's Elizabeth Berkley and Glee actress Amber Riley.