Princess Anna was born on 21 July 1616 at the Palazzo Pitti in Florence, then the capital of Tuscany. Her father was Cosimo II de' Medici, he had been the reigning Grand Duke of Tuscany since 1609. Anna's mother was Maria Maddalena of Austria, a daughter of Charles II, Archduke of Austria, and a sister of Emperor Ferdinand II. Her Medici and Habsburg ancestry was a common pairing among seventeenth century marriages in her family; indeed, she herself would come to marry a Habsburg, as would her daughter.

Her father died on 28 February 1621, causing her mother and grandmother Grand Duchess Christina to serve as regents until the majority of Anna's brother was reached. It was said that Anna and her sister Margherita inherited from Maria Maddalena her good qualities and marked abilities.

Following failed plans for Anna to marry Gaston, Duke of Orléans, she was instead engaged to Archduke Ferdinand Charles of Austria. In 1646, Anna left her native Florence for Innsbruck to be married. On 10 June, she was married to her double first cousin Ferdinand Charles, Archduke of Further Austria. He was the eldest son of Leopold V, Archduke of Austria and his wife Claudia de' Medici. Anna was thirty years old, while Ferdinand Charles was only eighteen. The match was negotiated by Ferdinand Charles' formidable mother, who had been regent of Further Austria and Tyrol since Leopold's death in 1632. Claudia had ruled the duchy well in her regency from 1632 to 1646, and was successful in keeping Tyrol out of the Thirty Years War. During the year of their marriage, Ferdinand Charles took over his mother's governatorial duties and became the ruler of Tyrol and Further Austria, as he was now of age. Anna and Ferdinand Charles had three daughters. The couple preferred the attractions of the opulent Tuscan court to the mountains of Tyrol, and consequently were more often at Florence than at Innsbruck. As a result, their eldest daughter was born in Anna's home court, not Ferdinand Charles'.

...
Wikipedia