Right-back Cassani, 28, spent last season on loan at Fiorentina and the switch has become permanent after he made 26 league appearances in their successful battle to avoid relegation.
Pinilla, meanwhile, moved to Cagliari in January on loan and made a big impression, scoring eight goals in 14 league appearances.
He is excited at having signed a permanent deal.
"This is just what I wanted," said the Chilean striker on the club's official website, www.cagliaricalcio.it.
"I have to thank Cagliari for the trust shown in me and Palermo for allowing me to leave the club.
"I believe this is the best place to continue my career."