The 27-year-old man was identified as Vladimir Arutyunian, an ethnic Armenian Tbilisi resident.
The reading of the verdict took more than an hour. Arutyunian's lawyers said they would appeal against the sentence.
Although Arutyunian initially confessed in a police video to throwing the grenade with a view to hurting Bush, he pleaded not guilty at his trial.
Georgian prosecutors say the grenade Arutyunian tossed at Bush and his Georgian counterpart Mikheil Saakashvili during a 10 May public appearance did not go off for technical reasons.
(Prime News/Rustavi 2/AP)