Maksim Chmerkovskiy, a pro dancer on DWTS, choreographed the couple's first dance, PEOPLE reports in this week's issue.
Clinton, 30, and her groom, 32, made a big splash at their July 31 reception with a sultry first dance.
"It was an amazing, funny, unexpected dance," a friend of the bride's tells PEOPLE. "Bill and Hillary seemed to love it."
There was lots of love that went around at the ceremony in Rhinebeck, N.Y. The couple, according to a guest, "are not two people who usually stand around grinning. But the whole weekend they radiated joy and happiness."
As for the food, the cake was a four-foot, nine-tier masterpiece of vanilla sponge cake, layered with dark chocolate mousse. It was gluten free, and the chefs Maarten and Frances Steenman, owners of La Tulipe Desserts, gave PEOPLE an exclusive look of their creation.
For many more inside details of Chelsea Clinton's lavish wedding, pick up this week's issue of PEOPLE, on newsstands Friday