After attending the Collegio degli Scolopi in Florence, he entered the Livorno Naval Academy in 1931, where he distinguished himself for perseverance and inventiveness.

In 1929, Tesei had the idea for the manned torpedo, from the Italian device used to sink the Austrian battleship SMS Viribus Unitis during World War I.

The SLC was extensively used in World War II by the Italian Navy and was used in the sinking of two British battleships in Alexandria.

On 26 July 1941, Tesei died in action during a manned torpedo attack on Malta (see Decima Flottiglia MAS#1941), for which he was posthumously awarded the Italian Gold Medal of Military Valour.

The modern Italian commando frogmen group Comando Raggruppamento Subacquei ed Incursori Teseo Tesei (COMSUBIN) is named after him.