"Today, we watched with great pride and overwhelming emotion as Chelsea and Marc wed in a beautiful ceremony at Astor Courts, surrounded by family and their close friends.
"We could not have asked for a more perfect day to celebrate the beginning of their life together, and we are so happy to welcome Marc into our family," Bill and Hillary Clinton said in a statement issued on Saturday night (local time) after the wedding, details about which were kept closely guarded till the end.
"On behalf of the newlyweds, we want to give special thanks to the people of Rhinebeck for welcoming us and to everyone for their well-wishes on this special day," Chelsea's parents said.
Among the guests were former secretary of state, Madeleine Albright, actors Ted Danson and Mary Steenburgen, film producer Steven Bing, Indian-American hotelier Sant Chatwal, who is close to Clinton family and fashion designer Vera Wang who designed Chelsea's dress, according to People Magazine.
Hillary wore an Oscar de La Renta.
"We want to wish them the best," Danson told People, "they are great kids, very family-oriented."
The guests must have had a personal connection to the bride or the groom to be invited. This is Chelsea's day, not her famous parents' day, the Washington Post reported, earlier in the day.
"They respect her and what she thinks... They want what she wants," said a family friend speaking on condition of anonymity. "They raised her to be her own person independent in thought."
Chelsea, 30, married Marc Mazvinsky, 32, who works at G3 Capital, a Manhattan hedge fund.
They were friends as teenagers in Washington, DC, and attended Stanford University together. Clinton completed her master's degree in public health this year at Columbia University.
The marriage is an interfaith marriage since the bride was brought up as a Methodist Christian and the groom is Jewish.
In an interview with NBC in Islamabad last week, Hillary expressed her support for the interfaith marriage.
"Over the years, so many of the barriers that prevented people from getting married, crossing lines of faith or colour or ethnicity have just disappeared," Clinton said.
"Because what's important is: 'Are you making a responsible decision? Have you thought it through? Do you understand the consequences?' And I think in the world that we're in today we need more of that," she had said.
"I was not invited to the wedding because I think Hillary and Bill, properly, want to keep this thing for Chelsea and her soon-to-be husband," President Obama had said.
Though he joked, "You don't want two Presidents at one wedding. All the secret service, guests going through (metal detectors), all the gifts being torn apart
"
Chelsea and Marc, who works at G3 Capital -- a Manhattan hedge fund, were friends as teenagers in Washington DC and attended Stanford University together. Chelsea completed her master's degree in public health this year at Columbia University.
The marriage at the Astor Courts -- which had been declared a 'no-fly' zone with hundreds of security personnel blocking all roads leading to the venue -- was an interfaith wedding since the bride was brought up as a Methodist Christian and the groom is Jewish. The ceremony was conducted by a rabbi and a reverend.
Citing the family, American media reported that the ceremony included a poem by Leo Marks titled, "The Life That I Have."
In an interview with NBC in Islamabad last week, Hillary had expressed her support for the interfaith marriage.
"Over the years, so many of the barriers that prevented people from getting married, crossing lines of faith or colour or ethnicity have just disappeared," she had said.
"Because what's important is: 'Are you making a responsible decision? Have you thought it through? Do you understand the consequences?' And I think in the world that we are in today we need more of that," she had said.
On Friday night, Bill and Hillary waved at spectators gathered near the venue as they arrived at the Beekman Arms Inn at the centre of Rhinebeck for a post-rehearsal dinner party.
Bill Clinton charmed the locals during a casual stroll through the town ahead of the wedding, saying that he was pleased with his daughter's choice of life partner.
"I like him (Mark) very much," a smiling Clinton said, adding, "I really do. I admire him. Hillary feels the same way."
Casual in jeans and a black golf shirt, the former President shook hands and greeted the crowd like he was back on the campaign trail, according to New York Daily News, which described Chelsea's marriage as the 'Wedding of the Millennium'.
Despite its persistence, the media, which had been swarming the small town, could not dig out too many details about the marriage.
Tight security kept the press away from the ceremony. Airspace above Rhinebeck had been closed for 12 hours from 3 pm local time on Saturday for the wedding.
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Image: Chelsea with father and former US president Clinton. A file picture