The 40-year-old - who is believed to have extended his terms until 2026 - replaced Joe Montemurro in the summer of 2021 and led Arsenal to within a point of Women's Super League glory in his debut season, as the North London giants finished second in the table behind Chelsea.
The Gunners only pipped Manchester City to the third and final Champions League spot on goal difference last term, but Eidevall ended the club's four-year trophy drought with victory over Chelsea in the Women's League Cup final, despite working around a number of severe injuries to key players.
Beth Mead, Leah Williamson, Vivianne Miedema, Kim Little and Laura Wienroither were among those to sustain serious problems, but Eidevall managed to lead a depleted Arsenal to the semi-finals of the Women's Champions League, where they lost 5-4 on aggregate to Wolfsburg after an agonising 3-2 second-leg extra-time defeat at the Emirates.
"I'm full of pride to have signed a new contract with this football club," Eidevall told the official Arsenal website. "I'm aware of the huge privilege and responsibility that comes along with my role at Arsenal. This is a special place with a special group of players and staff and we all believe there is a great future ahead of us here, so I am delighted to have agreed a new deal.
"We've made great progress on and off the pitch over the last couple of years and we are all working hard to continue that growth every single day. Our ambition is to be competing for the highest honours in women's football consistently and we all believe we are capable of achieving that.
"I'd also like to say a special thank you to our supporters. From the moment I arrived, I've felt your warm support and it means the world. Home or away, our supporters never fall short - to represent this club, this community, is an honour. Together, we can achieve so much."
Sporting director Edu added: "We're delighted to have agreed a new contract with Jonas. This is an exciting time for our women's first team as we approach a new season and this announcement is an important sign of our renewed commitment to the journey ahead. As a club, our aim is to be challenging at the top of the game and Jonas will play a key role in us achieving that."
Finally, Head of Women's Football Clare Wheatley hailed the "real progress" Arsenal have made under the Swede's stewardship and expressed a desire to work with Eidevall for years to come.
"Jonas is a crucial part of what we are building here at Arsenal and we're very pleased to say he has signed a new deal with us," Wheatley said.
"He has overseen real progress since joining us in 2021, winning his first silverware and guiding us to the semi-finals of the Champions League last year. Jonas shares our ambitions for our club and we are looking forward to working towards them together over the coming years."
Eidevall - who previously took charge of Lunds BK and Rosengard in his native Sweden - boasts a record of 53 wins, 10 draws and 18 defeats from 81 matches in charge of the Gunners, but his side have endured a challenging start to the 2023-24 season.
Arsenal's Champions League adventure came to a premature end in the first qualifying round, as they lost on penalties to Paris FC following a 3-3 draw in 120 minutes, before being beaten 1-0 by Liverpool in Sunday's WSL opener in front of a record-breaking Emirates crowd.
The Gunners are next in action away from home against Manchester United on Friday night, before returning to the Emirates to meet Aston Villa on October 15.