The court said in its ruling that it concluded that all of Simpson's arguments for appeal were without merit.
The court ordered the conviction of Simpson's co-defendant Clarence "C.J." Stewart to be reversed and a new trial held.
The 63-year-old Simpson is serving nine to 33 years at a state prison. His co-defendant, Clarence "C.J." Stewart, is serving 7 1/2 to 27 years at High Desert State Prison northwest of Las Vegas.
Both men were convicted of kidnapping, armed robbery, conspiracy and other crimes for what Simpson maintained was an attempt to retrieve family photos and mementoes.
The racial makeup of the jury and the conduct of the judge were key issues in the former football star's appeal.
Clark County District Attorney David Roger has called the September 2008 trial contentious but fair, and the sentences just. He had urged the justices to deny both appeals.
Simpson attorney Yale Galanter characterized his client's conviction as prejudicial "payback" for his 1994 double-murder acquittal involving the 1994 slayings of his ex-wife, Nicole Brown Simpson, and her friend Ron Goldman in Los Angeles.
At a previous hearing, Justices Michael Cherry, Mark Gibbons and Nancy Saitta posed pointed questions about whether Stewart received a fair trial alongside Simpson.
Four other men took plea deals and received probation after testifying for the prosecution.
Stewart, 56, is a former Simpson golfing partner from North Las Vegas.