Police said two other victims were in stable condition, and three had been released from the hospital.
People inside Hot Yoga Tallahassee appeared to have fought the gunman in an effort to save themselves and others, Tallahassee Police Chief Michael DeLeo said.
Authorities say it's not clear why he carried out the attack.
About a dozen people were inside Hot Yoga when a man with a black bag walked in around 5:30 p.m., the Tallahassee Democrat reported. Police have also obtained multiple search warrants on his electronic devices and social media profiles.
Florida State University President John Thrasher says Van Vessem and Binkley had ties to the university.
A Tallahassee police spokesman would not confirm or deny the videos were Beierle's, but biographical details mentioned in the videos match known facts about Beierle.
According to BuzzFeed News, Beierle posted several videos to a YouTube channel in 2014 that show him ranting about "whores" and "sluts". His likeness matches that of a man in a video expressing hate towards black people.
A woman who filed a police report against Beierle told The AP she's never forgotten how "creepy" he was. "Made another date, didn't show up". They told her the shooter kept coming in and out of the studio. "That was me, certainly, as an adolescent", he said. Rodger had written a manifesto in which he lamented his virginity, which he blamed on the "cruelness of women". "This endless wasteland that breeds this longing and this frustration".
"All evidence points to a single actor who has stayed on scene and is deceased at this time so there is no additional threat to the public", Mr DeLeo said. Rodger is lionized in the "incel" or "involuntarily celibate" community.
Ms Megan Nixon said she was eating at a restaurant underneath the studio when she heard shooting and people running upstairs. "They are showing up today because they want to show their love and support and that to me was just gosh overwhelming, because I can't imagine the things they have gone through and they continue think about other people". You could see her life shines through just about everybody she met.
After spending the summer studying in Germany, Binkley was back in town for what could have been her previous year in school. Our hearts are filled with sorrow and prayers for her family. It's an attack on peace.
They reportedly told him the shooter was a tall man with a beard.
Dr. Nancy Van Vessem was also killed in the shooting.
The 2012 incident happened in a dining hall on Florida State's campus.
All three had connections to Florida State University - Beierle a former student, Dr Van Vessem an employee and Ms Binkley a current student - but it is unclear if they knew one another.