Sa Pinto replaced Farhad Majidi, who left the Blues after inspiring Esteghlal to the title in the Iranian league.
The 49-year-old coach started his coaching career in Sporting CP in 2012 and has also coached Braga, Legia Warsaw, Vasco da Gama, Gaziantep and Moreirense.
Sa Pinto has penned a one-year deal with the option of a further year.
Esteghlal had also negotiated with Alex Nouri, Jose Morais, Reza Enayati and Javad Nekounam.