St Helens forward Mark Flanagan, Widnes prop Phil Joseph, Huddersfield prop Craig Kopczak and Warrington half-back Gareth O'Brien will join next season.
North Queensland stand-off Robert Lui and Penrith Panthers prop Ben Murdoch-Masila have signed from NRL clubs.
Prop Olsi Krasniqi has agreed a two-year deal after joining in June.
Sheens, 64, coached Australia to World Cup victory in 2013 and joined Salford permanently in June after an initial advisory role.
He could not stop Salford finishing in the bottom four, but after head coach Iestyn Harris left he assisted Ian Watson as they secured a Super League place for next season by finishing third in The Qualifiers.
Watson will remain in charge of the team, with help from Sheens, Garreth Carvell and Martin Gleeson.
Sheens said of Salford's new additions: "The club has been working on a number of major signings in recent months and we are now in a position to make these announcements now our Super League status has been confirmed.
"I have been greatly impressed by the desire and the commitment of these players to join the club and they are all very determined to develop their careers further as the club continues to build," he told the club website.
Salford have signed six players for 2016 and agreed a three-year deal with director of rugby Tim Sheens, who has resigned as Australia coach.