The 28-year-old failed drug tests in February and May this year, and said he had been suffering depression.
"I have been suffering wellness issues, including depression, for a year and have been receiving professional assistance for the last few months," Slipper said in a statement.
"The advice is that I will make a speedy and total recovery.
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"In no way do my personal circumstances excuse my actions but I recognise now that I was not coping and that I need to properly address these wellness issues."
After a hearing last week, Slipper was given the minimum mandatory suspension in RA's illicit drugs policy, the governing body said in a statement.
He was also fined A$27,500 (15,730 pounds).
"We are extremely disappointed to be in this position today with one of our most senior international players having submitted two positive tests for cocaine," RA chief executive Raelene Castle.
"We are fully aware that James is dealing with very significant personal issues and we have been working with him since February on these matters.
"James has expressed his sincere remorse for his actions and for placing himself, Rugby Australia and the Reds in this very difficult situation."
Slipper, who made his international debut in 2010, has 86 caps for Australia and played more than 100 Super Rugby games for the Reds.
He was a surprise omission from the Reds team that lost 38-34 away to the Wellington Hurricanes last week, with the team citing "welfare reasons" for his absence.
Loosehead prop JP Smith started in his place.
Slipper is the second Wallabies and Reds player to fall foul of RA's illicit drugs policy in the past six months.
Utility back Karmichael Hunt was suspended by RA for four games earlier this year after he pleaded guilty to possessing a tablet of Xanax. Police dropped a charge of cocaine possession after arresting Hunt in December.
Hunt, who was also banned for six weeks in 2015 after pleading guilty to cocaine possession, has been out of the Reds side since.
(Reporting by Greg Stutchbury; Editing by Ian Ransom)
