The A's will play their final season at the Oakland Coliseum in 2024 and said they will work with MLB to identify "interim" locations to compete before opening a new ballpark on the Las Vegas Strip in 2028.
"We are excited to begin this next chapter in Las Vegas," owner John Fisher said in a statement.
"I want to thank the Las Vegas and Nevada community for welcoming us. We will continue to work hard to bring home more championships for our fans and for our new home in Vegas."
The move adds to Las Vegas' credentials as a new sports hub after the recent additions of NHL expansion team Golden Knights and the relocated NFL's Raiders and WNBA's Aces, and as Sin City prepares to host its first F1 race in 41 years this weekend.
Social media images showed Las Vegas' 'Sphere' structure lit up in the A's logo and the word 'Welcome' on Thursday.
The vote officially sets into motion the first MLB club relocation since the Montreal Expos moved to Washington, DC, in 2005 and became known as the Nationals.
It also marks a moment of heartbreak for the team's Oakland fans, many of whom had rallied to have their club stay put.
Fisher previously said he was unable to strike a deal with city officials to build a new stadium as the much-maligned Oakland Coliseum, which the A's once shared with the Raiders, developed a widely held reputation as MLB's worst ballpark.
"Today marks a significant moment for our franchise, and it's met with mixed emotions - sadness for this change and excitement for our future," said Fisher.
"I know this is a hard day for our fans in Oakland."