Zappacosta, 28, spent last term in Serie A with Roma but made only nine league appearances, having suffered a torn anterior cruciate ligament injury while in the capital.
The right-back joined the Blues in 2017, yet, having featured regularly across his debut campaign, he earned just one Premier League start in his second term.
He appears to have fallen down the pecking order under Frank Lampard after the emergence of Reece James, but is under contract until 2022.
Winger Pjaca, 25, has been at Juventus since 2016 after signing on a five-year deal from Dinamo Zagreb.
However, the Croatian has failed to establish himself in the Bianconeri's first team – for which he last played a Serie A game in March 2017 – and his spell at Genoa will be his latest loan away from the club after stints with Schalke, Fiorentina and Anderlecht.
Genoa, which finished 17th in Serie A last season and narrowly avoided relegation, begins the new campaign at home to Crotone on Monday (AEST).