The former Netherlands international had taken charge of the team on an interim basis after Jonas Eidevall resigned from his position as head coach in October.
Slegers, who was also at the Arsenal youth academy from 2006 to 2007, won the Women's Super League Manager of the Month award in December.
"I'm so excited to be continuing our journey together," Slegers said in a statement. "It's a wonderful honour to represent this club as head coach and I have so much belief in what we can all achieve together.
"Over the past few months, I've felt such a powerful sense of collective ownership and responsibility across our players and staff – that has been our strength and I know we will make sure we drive and nurture this feeling as we all move forward.
"We want to deliver something beautiful that's inspiring and leads to winning trophies..."
Arsenal, third in the Women's Super League with 21 points from 10 matches, next host bottom side Crystal Palace on Sunday.