The couple looked thrilled as they waved to a crowd of well-wishers after exchanging vows in the town of Königstein, near the bride's home city Frankfurt. Tuesday's civil service was the first of two wedding ceremonies for the duo.
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For her special day, Claire, 28, the daughter of telecomms millionaire Hartmut Lademacher, wore a silk ivory dress with a peplum feature and knee-length hemline. She finished off her elegant outfit with aquamarine earrings.
Guests included Felix' parents Grand Duke Henri and Grand Duchess Maria Teresa as well as his elder brother, the heir to the Grand Ducal throne, Prince Guillaume and his wife of one year, Princess Stephanie, who was pretty in a blush pink outfit.
It is thought that the groom asked his brother-in-law Felix Lademacher to be his witness, while Claire asked her sister-in-law Princess Alexandra to do the honours.
On Saturday the couple will be joined in marriage during a religious ceremony before 350 guests at the Sainte Marie-Madeleine de Saint-Maximin-la-Sainte-Baume basilica in the South of France.
After the wedding celebrations 29-year-old Felix plans to whisk his new wife off to a secret destination.
He told a local newspaper: "The day after our wedding we will depart on our honeymoon, and I will personally take care of the organisation. It is tradition in our family that the destination of the honeymoon is a surprise for the bride, that is only revealed at the last minute before departure..."
The latest addition to the Luxembourg royal family is brainy and beautiful. Claire speaks German, English, French and Italian. She is currently working towards a doctorate in the field of the ethics of organ donation at a university in Rome.