The Court of Arbitration for Sport (CAS) has ruled that Jack's two-year doping ban, which she has served, will stand.

Jack was initially banned for four years after testing positive to Ligandrol on June 26, 2019, almost three weeks before the world swim titles in South Korea.

The Queenslander appealed her ban to CAS which reduced her suspension to two years, finding Jack did not knowingly ingest the substance.

But Sport Integrity Australia (SIA) appealed that reduction, citing a need for clarity regarding anti-doping legal principles.

CAS on Thursday rejected the SIA appeal, meaning Jack can return to the sport.

"After a 2 year and 3 month battle, I have finally received my final decision that my appeal case has been dismissed by the Court of Arbitration," Jack posted on Instagram.

"I am now free to do what I love with no restrictions and am so overwhelmed with joy.

"I am now going to take some time to myself to cherish this moment and reflect on what I have endured. The nightmare is finally over.

"Thank you to everyone who has stood by me, supported me and help me overcome this challenge.

"I will speak more in the future, now is not the time ... but watch this space, it's only the beginning."

SIA chief executive David Sharpe said Jack's case was now closed.

"This matter wasn't about pursuing an individual athlete," Sharpe said in a statement.

"It was very much about providing clarity and consistency to athletes and sports in the application of the World Anti-Doping Code."

SIA was established in July last year, taking over management of the former Australian Sports Anti-Doping Authority among other agencies of the federal government.

CAS on November 24 last year published its full decision, noting Jack admitted she didn't know how the substance was in her system but suggested three possible sources for her positive test.

Jack suggested supplements she took was could have been contaminated at manufacturing.

Another possibility was the supplements were contaminated by being prepared or mixed in a blender that may have been contaminated or contained Ligandrol.

A third possibility was Jack may have come into contact with the Ligandrol or ingested it as a result of using a pool and/or gym open to the public in Townsville or Cairns while training before the 2019 world championships.

Australian Associated Press