Tremain, who played four ODIs in 2016, took 209 Shield wickets at 23.79 in six seasons with Victoria and will add further depth to the New South Wales attack.
"I hope that if I can continue providing that service then I'll contribute to the squad's success," Tremain said. "The wheel doesn't need to be reinvented. Work hard, play well, lead from the front and win games of cricket for NSW.
"Sydney is where my cricket career was forged, but it's fantastic being so close to family back at Yeoval [in Central West NSW] where it really all started. We were happy in Melbourne but with a young son and a nine-hour drive between him and his grandparents, we limited their interaction. Now we have the opportunity to grow a better relationship between Noah and his grandparents."
Tremain and Zampa are among four new full contracts handed out by New South Wales for the 2020-21 season which also include batsman Daniel Solway who scored a century on his first-class debut against South Australia and averaged 55.33 for the season. Allrounder Nathan McAndrew also gets on the list.
There will be renewed competition in the spin department this season following the release of Steve O'Keefe. Nathan Lyon is likely to be available for the first part of the season before the Test matches begin while the key motivation behind Zampa's move was to play more first-class cricket.
When Australia aren't in action New South Wales can field a team that resembles an international outfit with seven CA contracted players in their squad while Sean Abbott and Kurtis Patterson have also recently played at the top level.
New South Wales squad Sean Abbott, Harry Conway, Trent Copeland, Pat Cummins*, Ben Dwarshuis, Jack Edwards, Mickey Edwards, Matthew Gilkes, Ryan Hackney, Liam Hatcher, Josh Hazlewood*, Moises Henriques, Daniel Hughes, Nick Larkin, Nathan Lyon*, Nathan McAndrew, Peter Nevill, Kurtis Patterson, Daniel Sams, Jason Sangha, Steven Smith*, Daniel Solway, Mitchell Starc*, Chris Tremain, David Warner*, Adam Zampa*
Rookies Oliver Davies, Ryan Hadley, Baxter Holt, Arjun Nair, Lachlan Hearne, Tanveer Sangha