Montemurro confirmed his departure from Arsenal in March and left the club in May after leading them to a third-placed finish in the 2020-21 WSL season. He later took over at Juventus Women.
"I feel honoured to be taking this role. Arsenal have a rich history, more successful than any other women's team in England. I want to add to these honours," Eidevall said in a statement on the English club's website.
"It's super important that we win, and we will be very ambitious about that, but it's even more important that we live the values and defend the club badge on a day-to-day basis. I cannot wait to do that at Arsenal."
Eidevall began his management career as an assistant coach at men's side Lunds BK. He took over as head coach three-and-a-half years later and guided them to the 2009 second-division crown.
He then joined the Rosengard women's team as an assistant and later as head coach, guiding the team to Damallsvenskan titles in 2013 and 2014.
After a spell as assistant manager to Henrik Larsson at Helsingborgs, Eidevall returned to Rosengard and led them to the 2018 Swedish Cup and their first league championship in four years in 2019.