Eidevall, 38, joins Swedish club Rosengard after helping club Malmö reach the quarter-finals of the Women’s Champions League last season.
He succeeds Joe Montemurro, who left Arsenal this summer after guiding the Gunners to the 2018-19 Women’s Super League title and the Continental League Cup in 2018.
After first coaching men’s football, Eidevall joined Rosengard first as an assistant and then as a head coach, winning back-to-back titles in 2013 and 2014.
He had a brief stint as Henrik Larsson’s assistant at Helsingborgs, before returning to Rosengard and leading them to the 2018 Swedish Cup and their first league title in four years in 2019.
“Arsenal have a rich history, more success than any other women’s team in England,” said Eidevall.
“I want to add to these honors. It is very important that we win, and we will be very ambitious about it, but it is even more important that we live the values and uphold the club’s badge on a daily basis. I can’t wait to do this at Arsenal. “
Arsenal chief executive Vinai Venkatesham said Eidevall was the “top candidate”.
“He will bring the style of football that Arsenal fans want to see,” Venkatesham said. “He’s someone who likes to play up front, fast, attractive and attacking football.
“What really came out of all our interactions with Jonas was how much he wanted to join Arsenal and his desire to be a part of this club, his desire to be part of our future and to help us achieve our ambitions for the future. We are therefore delighted that he is joining us. “