Oscar Pistorius -- Bail GRANTED!

A judge just GRANTED Oscar Pistorius bail, saying the Olympian is NOT a flight risk. And get this ... bail was set at $112,771.

Pistorius was in court -- along with 2 members of Reeva Steenkamp's family -- as the decision went down. Pistorius' family and friends were cheering the decision in the courtroom.

The judge said it was highly improbable Pistorius could flee the country, given his fame and the fact that he's a double amputee. As Pistorius' lawyer noted, going through airport security would trigger multiple alarms.

And, the judge said, the prosecutor did not prove Pistorius had a propensity for violence -- meaning he would probably not kill again while out on bail.

Before ruling, the judge asked the prosecutor an interesting question -- If Pistorius' story was that he believed an intruder was in his bathroom, why didn't he "stage" a break-in to make his story more believable? The prosecutor conceded, "The fact that we have only one survivor of that tragic night is difficult for the state."

The prosecutor argued ... proving premeditation doesn't mean Pistorius had to plan the murder the night before ... "He planned it that night when she locked herself in [the bathroom].

Pistorius' lawyer suggested that the charge should be lowered -- to "culpable homicide" -- meaning the Olympian didn't have the intent to kill Steenkamp at all but that it was a "tragic mistake."

And Pistorius' running coach said before today's hearing if he gets out on bail, he'll train Pistorius to "get his mind kind of clear."