The Rome side had previously announced that a deal was in place to purchase versatile right-sided player Basta, who has been at Udinese since 2008.
Lazio president Claudio Lotito also revealed on Monday that Parolo's transfer was imminent.
Both deals have now been confirmed by Lazio, who have also purchased the full rights to Antonio Candreva during the transfer window.
"Lazio announces that it has filed contracts with Dusan Basta and Marco Parolo," read a statement on the club's official website.
Basta scored three goals in 30 appearances for Udinese last season, and ends his six-year association with the Friuli club.
Italy international Parolo was also a regular at Parma, the midfielder featuring on 36 occasions and contributing eight goals before representing his country at the FIFA World Cup in Brazil, featuring as a substitute against England and Uruguay.
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