The 27-year-old will be available for up to 10 Specsavers County Championship matches in the first half of the season and could also feature throughout the group stage of the Vitality Blast.
The paceman has not represented his country in the past five years having played three Twenty20s and one ODI in 2014, but continues to be a major contributor at domestic level.
In the 2018/19 Sheffield Shield he took 37 wickets at 22.29 for runners-up New South Wales, including six in the final against Victoria. He also finished as second highest wicket-taker in the previous edition of Australia's T20 Big Bash League, with 22.
"I'm really excited to join Derbyshire and have the chance to play some good county cricket with them," said Abbott.
"It's a good mix in the squad and I want to lead from the front and hopefully help the younger lads in their development at the same time, whilst having team success along the way."
Ahmad snapped up by Gloucestershire
Afghanistan spinner Qais Ahmad has signed for Gloucestershire.
The 19-year-old leg-spinner made his Test debut in September but remains a relatively inexperienced performer, with just 12 first-class appearances under his belt as well as nine List A matches and 35 Twenty20s.
The considerable excitement around the teenager was reflected in the recent draft for The Hundred, where Welsh Fire drafted him in the fourth round.
He has signed up for the entirety of the Vitality T20 Blast and will also be available for the final six games of the Specsavers County Championship as his new side look to establish themselves in Division One following last season's promotion.
"It is a great honour for me to join Gloucestershire after they had such a successful 2019," said Qais.
"Having played T20 cricket around the world I have always wanted to play first class cricket in England to develop my red ball skills."
Head coach Richard Dawson added: "I'm delighted that Qais has agreed to join us for next season as the club enters it's first season in Division One since 2004.
"We had a very strong season in 2019 and Qais will help take us to the next level in both the long and short formats with his game-changing skills. He's one of the most exciting young spinners in the world."
