Vogel signed a multi-year contract, but the terms of that deal haven't been released.
He's the 27th head coach in Lakers history.
Vogel last coached for the Orlando Magic from 2016 to 2018. He went to Orlando following five-plus seasons leading the Indiana Pacers, including trips to the Eastern Conference finals in 2013 and 2014. He has a career record of 304-291.
"Our guys are going to be coached very hard," Vogel said at Monday's press conference, which LeBron James attended but did not speak.
Lebron James here watching the press conference introducing his new coach, Frank Vogel. pic.twitter.com/KJAl5V8Uv1— Ashley Brewer (@abc7ashley) May 20, 2019
"Coach Vogel has a proven track record of success in the NBA Playoffs," general manager Rob Pelinka said in a statement. "He reflects the core qualities we were looking for in a head coach - including detailed game preparation, extreme hard work, and holding players accountable to the highest basketball standards."
The Lakers have missed the playoffs six straight seasons, ending this past year with a 37-45 record. The drought was expected to end this season, but injuries to James, Lonzo Ball and Brandon Ingram, as well as internal discord, resulted in a 37-45 record. Vogel will be the Lakers' sixth coach since Phil Jackson stepped down after the 2010-11 season.
The Lakers have yet to announce the hiring of Jason Kidd as an assistant on Vogel's staff. Kidd - who interviewed with the Lakers last month - was a head coach in Brooklyn and Milwaukee but was fired by the Bucks during the 2017-18 season. He has a 183-190 record.
Los Angeles expects to have more than $40 million in salary cap space this summer and will likely resume its pursuit of New Orleans' Anthony Davis either around the draft or the July 1 start of free agency. The Lakers will likely try to land Kawhi Leonard and other big names who might be willing to play with James.
They also have five players - Rajon Rondo, Kentavious Caldwell-Pope, Lance Stephenson, JaVale McGee and Tyson Chandler - who were on one-year or expiring contracts.
The Associated Press contributed to this story.