The 37-year-old model - who lost a baby boy named Jack in September 2020 due to pregnancy complications - is feeling excited about the latest addition to their family.
A source shared: "They both really wanted to add another baby to the family. It's been a long road."
The insider told “PEOPLE” that Teigen - who also has Luna, six, and Miles, four, with John - and her baby are both "doing well".
Teigen’s and Legend’s two older children are "excited" by the new arrival, too.
The source said: "It's such an amazing way for them to start the new year."
In September, Legend admitted that the pain of losing his son would never "completely go away".
The award-winning musician explained that the heartbreak would stay with him for the rest of his life.
He said: "That pain is never going to completely go away. You're never exactly the same after you lose someone."
The pair have managed to cope with their heartbreak thanks to their other children.
The 44-year-old music star - who has been married to Teigen since 2013, explained: "To have two little ones that we could dote on and nurture and enjoy. They bring us so much joy.
"We just were able to hold each other through what was a very tough time."
Legend also revealed that he tempered his own excitement after Teigen announced her latest pregnancy.
The “Who Do We Think We Are” hitmaker said: "There's always this sense of cautious optimism, because you know what it's like to lose one."