The X Factor mogul was snapped holding his precious cargo in a carry seat as he exited his plush hotel on Thursday (20 February).
Just how adorable is Eric?!
British Simon became a father for the first time on Valentine's Day when girlfriend Lauren Silverman gave birth to Eric, named after Simon's late father.
Record mogul Simon set tongues wagging that his little one was on the way when he skipped a Britain's Got Talent audition day to make a dash across the Atlantic to be by Lauren's side at the birth.
He confirmed the birth via Twitter, writing: "Very happy to say Eric was born at 17.45pm. Healthy and handsome. Lauren in great shape. Thanks for all of your kind messages. Named after my dad."
Proud dad Simon hasn't been able to resist posting various shots of his adorable son to Twitter (which we're very thankful for!) and in one particularly sweet photo he added the caption: "I never knew how much love and pride I would feel."
Earlier this week, it was reported that Simon and Lauren had applied for a passport for little Eric, suggesting he'll be making his first trip to Simon's home, England, when he's a bit older.
Simon may be basking in the joy of new fatherhood but he's still keeping an eye on business, tweeting on Wednesday night (19 February) how proud he was of One Direction's success at the Brit Awards 2014.
They picked up gongs for 'Global Success' and 'Best British Video' for 'Best Song Ever'.
"Congratulations One D! Global success of the year. So happy for you," he wrote. "A huge thank you to everyone who helped them achieve this. The greatest fans. Thank you everyone for voting for best video. It is a brilliant video. Congrats to the boys and Ben who made it."
More celebrities who have welcomed babies in 2014:
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