The X Factor mogul released the cute photograph last night and it shows his son lying in his cot with a knitted elephant and cuddly toy dog.
Alongside the snap, Simon commented: "Eric's new friends." Aww!
British star Simon became a dad for the first time on Friday - Valentine's Day - after his girlfriend Lauren Silverman gave birth in New York.
Clearly besotted, Simon soon released the first pictures of himself cuddling his newborn baby Eric, telling the world: "I never knew how much love and pride I would feel."
On Sunday, Simon, Lauren and Eric left hospital and headed home. In the early hours of yesterday, Simon also gushed: "The last three days have been incredible."
Simon had missed the Britain's Got Talent auditions in London on Friday due to Lauren's labour and instead jetted back to New York to be there for the birth.
Baby Eric weighed 6lbs 7oz when he arrived at 10.45pm UK time (5.45pm in New York) at Lenox Hill Hospital, NYC, two weeks earlier than Lauren's expected due date of February 28.
More celebrities who have welcomed babies in 2014:
Copyright: Rex Features WENN/Matthew Taylor/Daniel Deme/Josiah True/Matthre Taylor/Joe