The pair met in May when they both joined Simon Cowell on the X Factor USA judging panel. However, their time together was shortlived as Cole was axed from the show late last month.
Adul wrote on Twitter: "Wow it's already June 30th! Happy Birthday to the beautiful & multi-talented Cheryl Cole. I miss your fiery sweetness! (sic)".
Further praising the Girls Aloud star, Abdul added: "Cheryl Cole - You're the very stuff of stardom sweetheart - I'm anxiously waiting w/ open eyes& ears to see what you have in store! Love u!"
Cole, who turns 28 today, will reportedly celebrate her birthday with a private party costing £20,000 tomorrow night.
Making her first appearance since leaving both the US and UK versions of The X Factor yesterday, Cole made the front pages of various tabloids after unveiling a new shorter, blonde haircut.
> Paula Abdul: 'Cheryl Cole is a delight'