Félix's parents Grand Duke Henri and Grand Duchess Maria Teresa announced the happy news in a statement released by the Grand Ducal Palace.
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Prince Félix and Princess Claire of Luxembourg released a series of new photos to coincide with the birth of Princess Amalia
"The Grand Duke and Grand Duchess are very happy to announce the birth of the first child of their royal highnesses Prince Félix and Princess Claire. The baby was born on 15 June 2014 at the Grand-Duchesse Charlotte Maternity Wing at the Centre Hospitalier de Luxembourg.
Félix and Claire paid tribute to their respective mothers, Grand Duchess Maria Teresa and Gabriele Lademacher, with their daughter's middle names.
"The young princess will bear the names Amalia, Gabriela, Maria Teresa.She weighed 2.95kg and measured 50cm at birth."
The couple have been living in France since their wedding
The statement added that 30-year-old Félix was present at the birth and that "mother and baby are doing well."
Both Félix and Claire's parents are overjoyed at the couple's new arrival and the royal announcement ended, "The Grand Duke and Grand Duchess as well as Mr and Mrs Lademacher and their families expressed their best wishes and joy at the happy news."
The new arrival is the third grandchild for Grand Duke Henri and Grand Duchess Maria Teresa as their son Prince Louis has sons Gabriel, eight, and Noah, six, with his wife Princess Tessy.
For the service in the 13th-century Sainte Marie-Madeleine basilica, the bride was a vision in a chantily lace gown by Lebanese maestro Elie Saab, which was dotted with crystals and mother of pearl sequins. The fairytale look was topped by a diamond tiara, lent by her mother-in-law.