Matthew Finch, 29, penned the song for daughter Ivy after he and wife Abigail suffered several sleepless nights following her birth on August 29.
After singing traditional lullabies which failed to get Ivy to drop off, he decided to write his own about what he thought she would dream about.
He uploaded the 3.09-minute video of himself singing the song to Ivy and within hours it went viral after being shared 10,000 times from fans across the world.
Matthew, a trainee development advisor, has now been bombarded with requests from new parents from around the world to write and perform more lullabies.
Yesterday (Fri), Matthew, from Hollywood, Birmingham, said: “I used to be in a band when I was younger so like singing.
“When Ivy came home I tried singing traditional lullabies to get her off to sleep but they never really worked.
“One of my friends half jokingly challenged me to write a song for Ivy and I thought I’d give it a go.
“I pulled out my guitar late on Friday and started playing around.
“I’ve never been good at the soppy songs, and as Ivy was sleeping next to me I just started to wonder what she was dreaming.
“Then I thought if I was a child and I was dreaming, where would I like to go.
“Once I was done I played it to Abi and she said I should put it on Facebook.
“At first I just posted it to a few friends and family, and then they started sharing it.
“I posted it quite late in the evening and got the initial likes from family and friends, and I just thought that it was because when you post a video of a baby to the internet you’re going to melt hearts.
“Then we woke up the next morning and we couldn’t believe how many people have seen it.
“My wife’s still a bit shocked, and my mate who challenged me thinks he should get more credit.
“I’ve been blown away by the response, really overwhelmed especially with all the nice comments that I got.
“I like to think that Ivy helped, I was looking after her at about 11 o’clock at night and she was nodding to the bits she liked and stopped to the bits that she didn’t.
“I write a lot of songs anyway, but I just write what inspires me. I guess now I have a baby daughter I might write more child songs – I’ve never written any before.
“I’ve been contacted by parents from all over the world asking me to send them audio clips to help their kids get to sleep.
“Ivy really loves music, hopefully she’ll be a musician. She’s already a star.”
Matthew’s Facebook page has been deluged with comments from parents begging him to upload more songs.
User Janet Bradley, from Adelaide, Australia, wrote: “OMG please write more songs Matt, your voice is hypnotic.
“I played your song to my baby boy and he slept right through for the first time in six months!!! You are a genius.”
Meanwhile fellow user David C, from Dublin, wrote: “Matt, I don’t know you but you are a godsend. Dunno what your secret is but your song got my two girls to sleep after a few minutes. Move over twinkle twinkle, there’s a new ‘star’ in town.”
IVY’S SONG LYRICS
“Where will you go when you close your eyes?
“Will you swim down in the sea?
“Will you hide with the turtles, swim round and round in circles,
“Will you bring something back for me?”
The final verse goes: “Oh you drift off to dream land,
“Have all the fun that you could have,
“But I hope that you will be back soon.”