Sarah Jessica Parker is one sexy mama now.

The Sex and the City siren gave birth to a bouncing baby boy in the wee hours yesterday morning at Lenox Hill Hospital on the Upper East Side, sources said.

A placard on the door to the star's private, heavily guarded sixth-floor room revealed the baby's name, "David Perkins Broderick."

Parker, 37, is married to baby-faced stage and screen actor Matthew Broderick.

Parker apparently delivered her first child with relative ease, "pushing for just an hour," one source told The Post.

She and her hubby arrived at the hospital with two cars full of security guards in tow and were immediately whisked upstairs, sources said.

After the birth around 3 a.m., the newborn did not go to the nursery with other babies but instead remained in the room with Parker, as is customary in the case of moms in private rooms, sources said. The famous family's littlest show-stopper apparently debuted right on time.

Parker -- among the latest stars to make pregnancy fashionable by sporting low-cut, designer duds over her expanding belly -- was due to give birth at the end of this month.

The ecstatic new parents were already receiving warm wishes from relatives and friends -- including Sex and the City co-star Cynthia Nixon, who herself is expecting.

Nixon was spotted slipping into the hospital to pay a quick visit to Parker and little David yesterday.

Baby Broderick is sure to be showered with expensive goodies from all, and it's likely he's already accumulated a hoard of homespun items, considering his mom is an avid knitter.

A bulging Parker was last seen in public early Saturday strolling through the city, with Broderick at her side. The night before, she and Broderick were spotted popping into Indochine for a quick, late-night snack.

Both she and her hubby had kept much about the pregnancy under wraps, including the sex of their new bundle of joy.

Parker balked at even the thought of allowing writers to incorporate her pregnancy into the story line of her hit HBO show, in which she plays frenetic sex-columnist Carrie Bradshaw.

Neither the pair's reps nor the hospital would comment on the joyful event.

The first photos of the couple's new bundle could fetch more than $200,000 for some lucky paparazzi, according to some estimates.