[2][3] She was the first child and eldest daughter of Ferdinand Charles, Archduke of Further Austria and Count of Tyrol, by his wife and first-cousin Anna de' Medici.

Her parents failed to produce a male heir: after Claudia Felicitas, they had only two other daughters, one who died immediately after birth (19 July 1654) and Maria Magdalena (17 August 1656 – 21 January 1669).

[9] After the extinction of the Tyrolean branch of the House of Habsburg in 1665, Further Austria and the County of Tyrol came under the direct control of Emperor Leopold I. Anna de' Medici tried to protect the rights of her daughters.

The dispute with the imperial court ended only after the wedding of her eldest daughter with the emperor; after her marriage, Claudia Felicitas retained the title of Countess of Tyrol.

[10][11] From his first marriage with Infanta Margaret Theresa of Spain, Leopold I had four children (including two sons), but all except the eldest daughter, Archduchess Maria Antonia, died shortly after birth.

He was the last of the male Habsburgs, besides the sickly King Charles II of Spain, and thus was in dire need of a male heir;[12] so shortly after his first wife's death (12 March 1673), the emperor (despite his deep mourning) was forced to start looking for a new wife and opted for Claudia Felicitas, his second cousin (both being great-grandchildren of Charles II, Archduke of Inner Austria),[13] who also could bring to him her possible rights over the Tyrol.

[11] The princess, with the consent of her relatives, immediately agreed with the proposal, rejecting other suitors of her hand, including the widower James, Duke of York and future King of England and Scotland.

[14] While praising his prospective bride's youth, attractiveness, and awareness of the great status it implied to be Holy Roman Empress, Leopold I added that she was "not like my only Margareta"[15] in a letter on 12 July 1673, three months before the wedding with Claudia Felicitas took place.

[20] At the time of her first pregnancy in 1674, a poem appeared in Vienna describing the intimate relationship of the imperial couple, written in cross form according to the rules of the "Rösselsprung" puzzle.