The defendant, Vladimir Arutyunyan, "is sentenced to the highest form of punishment - life in prison", the presiding judge in his trial said on Wednesday.
"He was found guilty on eight charges from the criminal code and four of them demand the highest form of punishment," Judge David Dzhugeli said.
Attempted assassination was one of the four charges calling for a life sentence, the judge said in pronouncing the sentence. The others included the killing of a police officer, terrorism and treason.
Arutyunyan said he would appeal the sentence. "I don't consider myself a terrorist, I'm just a human being," he said after Dzhugeli read the sentence.
"[Artyunyan] was found guilty on eight charges from the criminal code and four of them demand the highest form of punishment"
"I will appeal to all the international courts and organisations."
Arutyunyan was arrested last July in Tbilisi.
He was accused of throwing a live hand grenade that police found unexploded near a platform where George Bush and Mikhail Saakashvili, the Georgian president, were standing to address a crowd of tens of thousands of people on a public square.
His arrest was preceded by a shootout that left the Georgian interior ministry's top anti-terrorism official dead.
Artyunyan's sentencing on Wednesday came after forensic investigators from the US Federal Bureau of Investigation provided DNA evidence last month linking him to the failed attack on Bush and Saakashvili.
The investigators said DNA found on a handkerchief in which the grenade was wrapped matched that of Arutyunyan.
One of the FBI investigators, Brendan Shea, told the court: "The probability that a match could occur at random is one in 24 quadrillion."
Another FBI investigator echoed the findings of Georgian investigators who said a handkerchief wrapped around the hand grenade may have prevented its detonation by slowing the device's trigger.
The rally in May was the highlight of the first visit by a serving US president to Georgia.