The newborn royal prince made his world debut Tuesday shortly after 6 p.m. local time (1 p.m. ET) Tuesday.

Prince William and Duchess Kate showed off their brand new baby boy on the steps of St. Mary's hospital as they exited the Lindo Wing, where Kate gave birth Monday.

"He's got a good pair of lungs on him, that's for sure," William told the screaming crowd as he and Kate beamed. "I'll remind him of his tardiness when he's a bit older."

"He's got her looks, thankfully," Will joked, tipping his head towards his wife, who wore a polka dot dress by British designer Jenny Packham for the occasion.

William's mom, Princess Diana, wore a green polka-dot dress when he made his first appearance outside the hospital.

The prince said the couple is still "working on a name." Prince Charles and Princess Diana, took a week to announce Will's name.

After their comments outside the hospital, Will and Kate took the prince back through the hospital doors, then emerged again with the baby safely in his car seat. William swiftly installed the car seat into the back seat of a waiting Range Rover before driving his new family home to Kensington Palace.

Kate's parents, Carole and Michael Middleton, visited the hospital Tuesday, speaking briefly to the gathered press on the way out. "He's absolutely beautiful," Carole said of the baby. "They're both doing really well. We're so thrilled."

William's dad, Prince Charles, and his stepmother Camilla visited a bit later. Charles chatted briefly with staff that was lined up on the steps before entering the building.

In a statement earlier Tuesday, William and Kate said "we would like to thank the staff at the Lindo Wing and the whole hospital for the tremendous care the three of us have received. We know it has been a very busy period for the hospital and we would like to thank everyone — staff, patients and visitors — for their understanding during this time."

Two gun salutes, including a 62-round salute at the Tower of London and another 95-round salute at Green Park, were fired in honor of the new heir to the British throne Tuesday morning.

The palace revealed news of the birth in a news release at 8 p.m. local time following a hospital stay that lasted more than 14 hours at London's St. Mary's Hospital, the same facility where Princes William and Harry were born.

The baby's birth was to be announced to the world in a formal declaration placed in front of Buckingham Palace on an easel, the same one used to announce Prince William's birth 31 years ago. But the palace released the news to the media first; the formal notice was posted a few minutes later.

While Duchess Kate, 31, remained in the hospital early Tuesday, thousands gathered outside the palace a short distance away, hoping to get a picture of the easel.

All of the queen's navy ships around the world were flying the Royal Navy Ensign from their main mast Tuesday to mark the birth. On HMS Kent, the crew paid a special eye-catching tribute by spelling out "A Boy" on the deck.

"We could not be happier," new dad Prince William said via his spokesman Monday.

Other couples who became parents on Tuesday will receive a special silver coin from Britain's Royal Mint.

First to receive the limited-edition silver penny were Marc and Beverley Miell, who gave birth to Adam Michael at 4:34 p.m. on Monday, just 10 minutes after the prince was born.

The infant will be third in line to the British throne, after his father and grandfather, Prince Charles. He is the first grandchild for both Prince Charles and the Middleton family.

Gifts and tributes poured in almost immediately from around the world. Monday evening, President Obama released a statement saying "Michelle and I are so pleased to congratulate The Duke and Duchess of Cambridge on the joyous occasion of the birth of their first child. We wish them all the happiness and blessings parenthood brings. The child enters the world at a time of promise and opportunity for our two nations. Given the special relationship between us, the American people are pleased to join with the people of the United Kingdom as they celebrate the birth of the young prince."

The baby's uncle, Prince Harry, remained at his military base in eastern England.

TODAY's Jillian Eugenios contributed to this story.