Abbott, 32, signed a Kolpak deal with the club in 2017, and has repeatedly maintained that he has no regrets about the decision to put a premature end to his international career.
He has taken 182 County Championship wickets in the past three seasons, and has the most wickets of any seamer in the country this year. He took 39 wickets at 22.71 in his 11 Tests for South Africa, but said that he had "never felt far away from being dropped" throughout his international career.
"I'm delighted to have signed a new three-year contract with Hampshire," said Abbott. "We have a great bunch of players and coaching staff all striving to achieve success for the club and I look forward to contributing to winning trophies in the coming years."
Asked by ESPNcricinfo last week if he had any regrets about giving up international cricket, Abbott said: "No, absolutely not. I haven't from the day I walked away.
"All I want to do is play cricket and enjoy it. Hampshire have brilliant in giving me a home since that day in early 2017. I love playing here, I love the club, my team-mates, and I couldn't be happier."
There remains uncertainty over whether Kolpak deals will be honoured after the UK leaves the European Union.
The ECB sent an email to counties earlier in the year explaining that in the event the UK leaves without a deal before the end of 2019, new applications for Kolpak/EU registrations would become void, although those with existing contracts would be permitted to continue under existing terms until the end of the 2020 season.
That said, the Daily Mail has reported that the ECB is considering an increase in the number of overseas players permitted in the County Championship from one to two, and that several contracts contain clauses that would trigger a switch to overseas status after Brexit.
Hampshire's press release made no mention of Abbott's Kolpak status, nor the possibility that the final two years of his new contract could theoretically be rendered void if no such clause exists.
Rilee Rossouw, who signed for Hampshire at the same time as Abbott, will not play red-ball cricket for the club next year. He returned to South Africa after the culmination of the Vitality Blast group stages, and is expected to return to play in the Blast in 2020, though it remains unconfirmed whether he will do so as an overseas or a local player.
It is unclear whether Rossouw intends to resurrect his international career - which may prove tricky after the circumstances of his departure - or instead to continue plying his trade on the global T20 circuit.
The club's director of cricket, Giles White, said he couldn't "speak highly enough" of Abbott.
"He has once again shown what a valuable asset he is to the team," White said. "He continually puts in match winning contributions, he is a great role model for the younger players and he shows a great passion for playing for the club.
"For all these reasons we are delighted he will be with us for the long-term."