The 16-year-old singer wowed the judges with her stripped-back version of the 1998 track during last night's (September 23) Boot Camp episode.
"Went on Utube 2 c young girl sing Believe!Tears came 2 my eyes! So Touching! a Great version of a Great Song.WE Can Share It (sic)," Cher tweeted.
"I'm still pinching myself!" Henderson said in response. "To have the actual Cher tweet that she'd seen my performance was mind-blowing. I've been smiling all day. It is quite frankly unbelievable! I can't believe she cried."
Judge Nicole Scherzinger was also moved to tears during Henderson's performance, which secured her a spot at Judges' Houses.
"I had no idea I made her cry," she added. "I was lost in my performance and totally unaware of my surroundings. I feel honoured that my performance touched her so much. I hope people are crying tears of happiness!"
Henderson also praised fellow contestant Lucy Spraggan, describing 'Tea and Toast' as "so beautifully written and very sad".
She concluded: "I just want to say a big thank you. All the online supporters have really boosted my confidence and have inspired me to be the best musician I can be."
Watch Ella Henderson's performance of Cher's 'Believe' on The X Factor below: