Beaming Bill and Hillary leave $1,700-a-night hospital and daughter Chelsea after meeting grandson Aidan for the first time 

Hillary Clinton beamed a satisfied smile while husband Bill waved to well-wishers as they left the exclusive Manhattan hospital where they had met their grandson for the first time.

Surrounded by their Secret Service detail, the Clintons walked out of Lenox Hill Hospital in tandem early on Saturday evening, where daughter Chelsea had given birth to their first grandson, Aidan.

Appearing to be in fine spirits, the Clintons earlier issued a statement saying that they were 'overjoyed' to be grandparents again as Chelsea and her husband Marc Mezvinsky declared themselves, 'overwhelmed with gratitude and love'.

Chelsea, 36, first tweeted the news of the birth of Aidan Clinton Mezvinsky on Saturday morning. Their daughter and first child Charlotte was born in September of 2014.

Proud grandparents: Hillary and Bill Clinton leave the Lennox Hospital where their daughter Chelsea clinton just announced had her second baby in New York City

Second time around: Hillary Clinton is flanked by an agent of her Secret Service detail as she departs Lenox Hill Hospital on the Upper East Side of New York City

Pleased: Former President Bill Clinton prepares to get into his car and be driven away after seeing his daughter after she had given birth to her second child, a son

Chelsea Clinton (pictured earlier this month) has given birth to a baby boy named Aidan Clinton Mezvinsky

Clinton, who announced she was expecting in December, tweeted news of the birth on Saturday morning

The Lenox hospital is famed for its exlusive and elegant maternity suite. 

A concierge can accommodate any whim the family has, and a 24-hour food service reportedly will whip up everything from lobster to cheesecake, delivered straight to the suite’s kitchen.

The cost per night is upwards of $2,000.

Chelsea isn’t the only new celebrity mom to have stayed at Lenox Hill’s maternity ward dedicated solely to the rich and famous. 

In January 2012, Beyonce and Jay-Z welcomed their daughter Blue Ivy on the same floor. The couple occupied a double room that has since become known informally as the ‘Beyonce Suite.’

And Simon Cowell’s girlfriend, Lauren Silverman, gave birth to their son, Eric, at the hospital in February

Earlier, the Clintons released a statement, saying they were 'overjoyed to be grandparents again'.

'We are all over the moon as Chelsea and Marc welcome Charlotte's little brother to the world and grateful for our many blessings,' Hillary and Bill said. 

'Chelsea and Aidan are both doing well and enjoying this very special time together.'   

Luxury: The Lenox hospital on the Upper East Side of Manhattan is where the city's rich and famous choose to give birth 

Aidan is the second child for Chelsea, 36, and her husband Marc Mezvinsky. The couple's daughter Charlotte was born in September 2014

Chelsea, 36, announced in December 2015 that she was expecting her second child with hedge fund manager Marc.

'Next summer, Charlotte is going to be a big sister! Feeling very blessed & grateful this holiday season,' she tweeted, keeping the baby's gender under wraps. 

Hillary Clinton often brings up her 20-month-old granddaughter, who was born in September 2014, on the campaign trail.

The presumptive Democratic presidential nominee has said being a grandmother is like 'falling in love all over again'. 

'It's transformational and until you did it, it is hard to know,' she continued. 'And it has for me been an absolutely life-changing experience.'   

Hillary has said in the past she was curious to see how Charlotte would handle being a big sister.

'We are wondering how this very independent, very assertive little girl, Charlotte, how she's going to adjust to the new baby,' Clinton said during a campaign event earlier this month. 

Both of Charlotte and Aidan's grandparents have deep political ties. Mezvinsky is the son of former US Rep Edward Mezvinsky and former US Rep Marjorie Margolies-Mezvinsky

Bill and Hillary were doting grandparents the minute Charlotte was born, pictured here leaving Lenox Hill Hospital with Chelsea and Marc after her birth 

'That will be our next adventure,' Clinton said. 

'We talk to her about it. She seems to be less interested in that than she does in Elmo and other games and toys.' 

Chelsea and Mezvinsky, who wed in 2010, both appeared on stage with her mother earlier this month to celebrate her presumptive presidential nomination for the Democratic party.

Clinton said that night she wished her mother Dorothy Howell Rodham, who passed away in 2011, could be there that night to watch her make history. 

'I wish she could see what a wonderful mother Chelsea could become and meet her beautiful granddaughter Charlotte,' Clinton added. 

'I wish she could see her daughter become the Democratic Party's nominee.'  

This is Chelsea Clinton's second child with hedge fund manager Marc Mezvinsky (pictured together with their 20-month-old daughter Charlotte)

Chelsea and Mezvinsky, who wed in 2010, both appeared on stage with her mother earlier this month to celebrate her presumptive presidential nomination for the Democratic party