Simon Cowell and Lauren Silverman are "settling into their new life" with baby Eric.
The couple welcomed their son into the world last month and they're beginning to adapt to parenthood and having a young tot around the house.
A source told E! News: "It's a happy time. They're settling into their new life."
Meanwhile, five-week-old Eric -- who was named after Simon's late father -- doesn't seem to be giving his parents a difficult job as he's already a "good sleeper".
The source explained: "The baby's doing well, he's very strong. He can already hold his head up! He's not fussy and and he's a good sleeper."
Lauren's eight-year-old son Adam -- from her previous marriage with Andrew Silverman -- is also besotted with his new half-brother and recently jetted over from New York to spend the holidays with him.
The source added: "Adam came to London for his spring break from school. He adores his little brother and loves helping with him."
Simon, 54, and Lauren are currently living in London due to the music mogul's busy schedule, but they are planning on dividing their time between the UK and the US as Adam lives in New York on a permanent basis.