The 27-year-old has taken 137 wickets in 50 first-class matches for New South Wales, where he has played since making his debut in 2011.
He was part of the side which won the 2013-14 Sheffield Shield, in which he claimed 27 wickets at an average of 29.44.
Abbott also took 37 wickets in the 2018-19 season, as New South Wales finished as runners-up to Victoria.
His international debut came in 2014, as he claimed 1-17 for Australia in a six-wicket victory over Pakistan in Dubai.
Two further Twenty20s and an ODI debut have followed, while he was selected in the Australia squad for the recent T20 series against Sri Lanka.
Domestically, Abbott also boats a strong record in the white-ball formats, having taken 91 wickets in 79 T20s, at an average of 22.90, while playing in the Big Bash and the IPL.
He has been a consistent performer in the Big Bash, in which he finished as runner-up in 2015. He was the second-highest wicket-taker in the latest edition of the competition with 22 dismissals.
Known for his pace and bounce, Abbott will be hoping that his time with Derbyshire strengthens his case for international selection across all forms of the game.