Sanz, 51, has linked up with manager Slavisa Jokanovic and the Blades squad at the club's pre-season training camp in Malaga this week. He has signed a three-year deal.
Sanz had a previous spell in charge of Valencia's B team before becoming technical director at the Mestalla, where he assisted Javi Gracia.
He previously worked with Jokanovic during his time as a player with Tenerife.
Meanwhile, the Blades have appointed Rafa Cristobal as the new first team head of performance, while Marco Cesarini comes in as head of first team medical services.
Cristobal worked with Jokanović at Fulham, having previously held similar positions at Las Palmas, Alaves, Real Valladolid and Levante.
Italy-born Cesarini, who has worked in his homeland at AC Milan and Brescia, served under the Blades manager in both his previous jobs in England at Watford and Fulham.
Cesarini also had a spell at West Ham, while his last position was at Chinese club Henan Jianye.