Gobert finished with 97 first-team points and 196 points and as a result earned himself a $500,000 bonus from the Jazz. This is the Utah center's third straight first-team selection.
George, an Oklahoma City Thunder forward, had 96 first-team votes and 195 points, followed by Bucks swingman Antetokounmpo (94, 193).
Smart and Bledsoe both earned their first All-Defensive team selections.
The second team included the Golden State Warriors' Draymond Green and Klay Thompson, who earned his first selection. They were joined by the Toronto Raptors' Kawhi Leonard, the Philadelphia 76ers' Joel Embiid and New Orleans Pelicans guard Jrue Holiday, who earned a $100,000 bonus for the honor.
The teams were selected by a panel of 100 writers and broadcasters.
ESPN's Bobby Marks and the Associated Press contributed to this report.