The model and TV personality, who is married to singer John Legend, shared the heartbreaking news on social media.
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"We are shocked and in the kind of deep pain you only hear about, the kind of pain we've never felt before. We were never able to stop the bleeding and give our baby the fluids he needed, despite bags and bags of blood transfusions. It just wasn't enough," Teigen wrote.
"We never decide on our babies' names until the last possible moment after they're born, just before we leave the hospital," her statement said. "But we, for some reason, had started to call this little guy in my belly Jack. So he will always be Jack to us. Jack worked so hard to be a part of our little family, and he will be, forever."
"To our Jack-I'm so sorry that the first few moments of your life were met with so many complications, that we couldn't give you the home you needed to survive. We will always love you," the statement also said.
In a separate tweet, Teigen wrote "Driving home from the hospital with no baby. How can this be real."
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In a tweet, John Legend wrote "We love you, Jack."
Teigen was hospitalized over the weekend and taken to Cedars-Sinai Medical Center after suffering heavy bleeding during her pregnancy.
In a series of Instagram posts, the "Lip Sync Battle" host and mother to daughter Luna, 4, and son Miles, 2, Teigen shared updates of her health complications and said that she had been bleeding a "little bit less than a month."
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One month ago, Teigen announced her surprise pregnancy on Twitter, sharing a video of her sonogram with daughter Luna looking on. But not long after, she began sharing information about pregnancy complications that caused her to be hospitalized.
The couple revealed they were expecting in Legend's music video for the song "Wild."
Teigen thanked everyone for their prayers, writing "On this darkest of days, we will grieve, we will cry our eyes out. But we will hug and love each other harder and get through it."
Teigen has been open and honest about her struggles with infertility. She previously said she hopes her honesty and openness are empowering to other women facing the same struggle.