Five of the signings came via the transfer portal, while the team also snagged one high school recruit.
Pickett reportedly signed on to a four-year, $8.3 million deal with a guaranteed initial three years.
Gambino takes over after 13 years as the head coach at Boston College.
Sturtz spent three seasons at Penn State as a forward from 2015-18.
The team announced the jersey numbers of its 2023-24 roster Monday, which includes 15 athletes.
The Nittany Lions will open the season against Le Moyne at Jeffery Field.