Surrounded by 400 friends and family, the former First Daughter, 30, was walked down the aisle by her emotional father Bill Clinton, in Rhinebeck on Saturday in a moving service held at Astor Courts.
Chelsea looked beautiful in a strapless silk organza gown, featuring a draped bodice and an embellished belt, created for her by coveted designer, and wedding guest, Vera Wang.
She exchanged vows with investment banker Marc, 32, under a flower adorned gazebo during the 5pm interfaith ceremony – Chelsea is Methodist whilst her new husband is Jewish – that included a reading of the poem The Life That I Have by British writer Leo Marks.
Shortly after the ceremony, a very trim Mr Clinton and his wife, Secretary of State Hillary Clinton, who wore a magenta Oscar de la Renta gown, released a statement.
"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," they said.
"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. 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."
Apart from the bride's famous parents, other high-profile guests included actor Ted Danson and his wife Mary Steenburgen, film producer Steve Bing, fashion designer Vera, and former Secretary of State Madeleine Albright.
The wedding reception reportedly featured a 20-piece band, which got guests up on the dance floor with some Motown classics and Frank Sinatra songs as well as music by Michael Jackson and U2.
In fact so much fun was had by all the guests – 73-year-old Madeleine is said to have been one of the most energetic dancers – that the party went on until three the next morning and the vegan wedding cake, thought to be in tiers of chocolate, was not cut until midnight.
Chelsea and Marc, who wore a tuxedo designed by Burberry's Christopher Bailey, have been friends since they met at a conference in 1993 and remained close while they attended Stanford University.
In 2005 they began their romance and husband and wife have lived together in recent years in a downtown New York apartment along with their Yorkshire terrier Soren.