The new dad, 23, posted a series of sweet snaps from the hospital as he tenderly held his baby girl in his arms.
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The boxer starred lovingly at his newborn, who was wrapped in a small white towel.
He held her close to his chest and told fans that it was the “best day of his life”.
Tommy then posted a photo of Molly in her hospital bed, while she adoringly gazed at her daughter.
He penned a sweet message which read: “The best mummy in the entire world.
“Watching how you care for Bambi makes me love you more than I knew I ever could.
“You’re everything I could have dreamed of for a mum and a role model for our perfect girl.
“Thank you for making my dreams come true babe. I love you.”
In another snap, Bambie was peacefully asleep on Tommy’s chest, while the doting father closed his eyes for a moment.
He captioned it: “Daddy’s little girl. Forever.”
The couple announced the long-awaited moniker today after giving birth on January 23.
Molly-Mae shared a picture from the tot’s nursery that showed her name up in neon lights.
Fans have been desperate to guess the baby’s name for months and came up with a number of theories.
Now that the news is out, it’s polarised her fans with some loving it and others well, not so much.
Paris Fury wrote: “Her name is just as cute as her. Loved seeing yous today she is absolutely perfect x.”
The Love Island favourite confirmed her daughter’s arrival when she posted a sweet snap, which showed her cuddling her boyfriend Tommy Fury and their daughter in hospital, on Instagram.
Alongside it she simply wrote her little girl’s birth date and later shared: “I can’t believe we get to keep you forever.
“Becoming your mum has been the best thing to ever happen to me. It doesn’t seem possible but my love for you grows with each passing moment.
“There is no feeling like holding you in my arms little one, my heart literally explodes.
“Thank you for entering this world safely for us and blessing us with the gift of being your parents.
“We promise to love and care for you unconditionally forever.”