Agler has left Seattle to take over a Sparks team that went 16-18 en route to a fourth-place finish in the Western Conference in 2014.
"I am excited about the possibilities with the Sparks," Agler said in a statement. "I appreciate the opportunity provided to me from [General Manager] Penny Toler, and of course the ownership group led by Magic Johnson, Mark Walter and Stan Kasten. I am joining a franchise that has a championship heritage, a world-renowned ownership group and an internationally known brand."
Agler, 56, has served as the Storm's coach since 2008, guiding Seattle to the WNBA title in 2010. He has a 184-169 WNBA career coaching record.
Toler fired coach Carol Ross after the first half of last season and took over as the team's coach. Toler said she wasn't interested in remaining the team's coach.
"In what was a very extensive search to find a talented leader and winner to be our head coach, Brian stood out as the right person to lead the Sparks," Toler said. "A proven winner, Brian's experience and leadership will energize our offense and challenge our defense to return the Sparks to a championship caliber team."
The Sparks lost to eventual WNBA champion Phoenix Mercury in the first round of the playoffs.
The Associated Press contributed to this report.