Sullivan gave an interview this week where he confessed his kids "begged" him not to sign Snodgrass from Hull.
Responding on Twitter, Snodgrass wrote: "Everyone tagging me in this like you're all surprised. Thanks for your support MR CHAIRMAN."
Snodgrass is contracted to West Ham until 2020 but is unlikely to appear for them again. The Hammers will try to recuperate their original fee.
Aston Villa, where he is on loan for this season, are likely to try to make the deal permanent in the summer.