The 'So Macho' singer is a close friend of the TV mogul - and even dated him at the start of her career - and announced she will be godmother to the new arrival, who was born yesterday (14.02.14) in New York to Simon and his girlfriend, Lauren Silverman.
Sinitta wrote on Twitter: ''Sitting in. Fancu bar in london with a very handsome man waitinf to hear my God son has been born, bit tipsy,but not ruined..too late to fly (sic).''
The 45-year-old star alluded to the fact she had wanted to fly out for the birth, but had left it too late. However, she said Simon was keeping her informed from the US about how the birth was going.
Simon, 54, had been in the UK filming a new series of 'Britain's Got Talent' but flew to New York on a private jet as soon as he heard Lauren had gone into labour.
He was pictured smoking outside Lenox Hill Hospital in Manhattan shortly before the baby boy was delivered, weighing six pounds and seven ounces.
Simon later tweeted: ''Very happy to say Eric was born at 17.45pm. Healthy and handsome.
''Lauren in great shape. Thanks for all of your kind messages.''
The baby is named Eric after Simon's late father, who passed away in 1999.
His new album Underneath It All is out now.