"The Portuguese international will travel to Turin in the next few days to finalize the details of his move to the Italian team," Deportivo said on their official website.
According to reports in Spain, Andrade will join the Bianconeri in a deal worth 10 million euros.
Juventus are continuing their rebuilding in order to be competitive in the Serie A next season after a one-year spell in the lower division due to their involvement in the Italian match-fixing scandal.
Having missed out on the chance to sign Argentinean defender Gabriel Milito due to Real Zaragoza's high financial demands, Juventus turned their attention towards Andrade, who is the second Portuguese to join the club after Tiago.
Andrade, who has over 40 caps for Portugal, joined Deportivo in 2002 after enjoying a fine two-year spell with Porto.