The pair were given permission to travel to Rome on Monday to undergo medicals, before both then agreed personal terms with the Partenopei, who are also hoping to sign Andrea Poli
The two players passed medicals with the Partenopei in Rome on Monday before sealing switches to the San Paolo.
"I want to make official the signing of Gamberini and Behrami," De Laurentiis told Radio Marte. "We are in Rome, where the two players have completed their medicals.
"We were pursuing the two deals for two months. Gamberini and Behrami are two players that I believe the Neapolitans can identify with, also for their human values.
"The two boys have made an extraordinary impression on me, having already begun to get to know them in recent weeks. They are two good guys and have great human qualities.
"This is an important factor, even before the technical side of things. They are all part of a series of assessments that we have done that make us particularly happy with the two new signings."
Gamberini, who has been capped eight times by Italy, has been at Fiorentina since 2005, while Switzerland international Behrami only arrived at the Artemio Franchi from West Ham in January 2011.
It is believed that Napoli, who won the Coppa Italia last season, are also on the verge of signing Andrea Poli from Sampdoria after the midfielder's proposed move to Inter collapsed.