President Josef Schnusenberg, who has already announced he will be stepping down at the end of his present term next June, will relinquish his operative duties with immediate effect and remain a symbolic president for the next 10 months.
Magath, who was already fulfilling the dual function of coach and general manager while taking his seat on the board, will be given responsibility for public affairs and marketing.
He will be assisted by Peter Peters, who will take responsibility for finances and personnel.
"We are certain that this change in structure will mean we are even better equipped," said chairman Clemens Tonnies on the club's website.
"We are also reacting to the expressed wish of Josef Schnusenberg."
Schnusenberg said he wanted to reduce his responsibilities in view of his retirement next summer.
"I will be 69 this coming February and the time has come to concentrate on other beautiful things in life," he said.
"That is why I have held lots of discussions recently about how we can successfully hand over my responsibilities. We all agreed that this should not just happen abruptly but should be a process.
"I have a good feeling about placing the operational responsibility into younger hands."
The changes mean Magath, who is one of only two coaches in German football to also be a general manager along with his successor at Wolfsburg Armin Veh, becomes one of the most powerful men at the Royal Blues.