The ruling by the Court of Arbitration for Sport (Cas) means the sprinters are free to race again immediately, and Powell will run in Lucerne on Tuesday.
Both were able to compete from 18 June pending the outcome of the appeal.
They both tested positive for the banned stimulant oxilofrine at last year's Jamaican national championships.
Personal bests: 100m - 9.72 secs; 200m - 19.90 secs
Medals: Olympics: 4x100m relay - gold (2008); World Championships: 100m - bronze (2004, 2008), 4x100m relay - gold (2009), silver (2007)
Cas said in a statement it had "decided to reduce their period of ineligibility to six months, which has been already served".
Powell, 31, called the initial suspension "unfair and unjust".
He wrote on Twitter: "Finally this weight has been lifted off my shoulders. Justice has been served. Now let's run!"
Powell and Simpson, 29, were given 18-month suspensions by the Jamaican anti-doping disciplinary panel in April, though both were backdated to end in December 2014.
Both argued their offence was minor because the positive results came from taking a contaminated version of Epiphany D1, a legal supplement.
In January, Powell testified that Canadian physical trainer Chris Xuereb provided him with nine supplements, including Epiphany D1, which Xuereb denied.
A stimulant drug banned by the World Anti-Doping Agency, the substance is an amphetamine found in some dietary supplements
It was developed to treat low blood pressure
The substance is thought to allow people to burn fat faster and lose weight, which is why it is present in some so-called sports nutrition supplements
It can also increase the rate at which the heart reaches its maximum performance during exercise
But Professor Wayne McLaughlin of Caribbean Toxicology told the Jamaican Anti-Doping Commission during Powell's trial that oxilofrine "does not improve speed"
Powell, the biggest name in Jamaican sprinting before the rise of double world and Olympic champion Usain Bolt, held the 100m world record between 2005 and 2008.
Training partner Simpson won silver in the 100m at the 2008 Olympics, and also has Olympic gold and silver medals from the sprint relay.
Both athletes will miss the Commonwealth Games in Glasgow as the Jamaican team was selected during their suspension.
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