Lijnders is leaving along with Jurgen Klopp as the team undergoes major changes.
"I am very proud to become the new head coach of FC Red Bull Salzburg," said Lijnders on the announcement.
"This is a real privilege for me. After PSV Eindhoven, FC Porto and Liverpool FC, I am now moving to another exceptional club with a really good structure and a particular focus on youth development.
"I want to develop a mentality with the team that places a lot of emphasis on attacking style of play and where passion and hunger for success are the basis of everything.
"Together with my assistant coach Vitor Matos and the entire support team, we will do our best to help the club continue to grow in an ever-changing football world.
"My family has visited the city before and was overwhelmed by its beauty and the friendliness of the people. That was the last and important step for me in choosing FC Red Bull Salzburg."