World governing body Fina had initially cleared Palmer in 2013 after the "low levels of a prohibited substance" found in her in-competition sample at the Barcelona world championships did not show up in other tests conducted around the same time.
In February this year, however, the World Anti-Doping Agency (Wada) obtained details of the case and subsequently asked the Court of Arbitration of Sport to order Fina to treat the case as an anti-doping violation.
Palmer then voluntarily withdrew from the Australian team for last month's world championships in Kazan and accepted a temporary suspension.
Fina's doping panel ruled on Tuesday she should receive only a warning and reprimand, with her results and prize money on the date of the test in 2013 annulled, Swimming Australia said.
The world governing body did not strip her of the 4x200m freestyle silver medal she won at Barcelona.
"Swimming Australia fully supported the process once the matter came before the Fina Doping Tribunal and accepts the findings," the governing body in Australia said in a statement.
"Palmer voluntarily accepted a provisional suspension until the matter was determined by the Fina Doping Panel.
"As such she is now able to compete whenever she decides to return."
Swimming Australia had previously said it was concerned at the two-year delay between the test and notification.
