The "Magic Mike" star, who has been dating the Brit since last year (18), gushed about her as she celebrated her 31st birthday on Wednesday, March 27.
Under a black-and-white photo of Jessie looking out of a window into sunlight, he wrote: "Wishing you the happiest day filled with all the love and all the light."
"You came into this world on this day and lit it on fire. You have blessed our eyes, our ears, our hearts and our lives. So thank you for just being you. You are so very special. Happy birthday Baby."
Tatum went public with the romance in November, seven months after his shocking split from his wife of nine years, Jenna Dewan.