Perotti joined the Serie A club on loan from Genoa in February and has now signed a full-time deal until June 2019.
The two-time Argentina international has made six appearances for the club, scoring his only goal in the 2-1 win over Sampdoria on February 7.
Zukanovic has featured four times for Roma and has also committed until mid-June 2019.
The Bosnia-Herzegovina international had initially signed on loan from Sampdoria in January.