[1][2] The toponym is most likely derived from Lombard tejee or tejé, referring to a "linden grove" that once grew in the area, or alternatively from Latin attegia "hut".

The site chosen was that of the family stables which he had built at Isola del Te, on the edge of the marshes just outside Mantua's city walls, as early as in 1502.

Once the shell of the building was completed, for ten years a team of plasterers, carvers, and fresco painters laboured until barely a surface in any of the loggias or salons remained undecorated.

In July 1630, during the War of the Mantuan Succession (1628–31), Mantua and the palace were sacked over three days by an Imperial army of 36,000 Landsknecht mercenaries.

The centers of the North and South facades are pierced by two-storey arches without portico or pediment, simply a covered way leading to the interior courtyard.