Former Liverpool and Leverkusen player Hyypia, who has been named team chief, and coach Lewandowski had taken over troubled Leverkusen in April on an interim basis.
They managed to turn their season around by helping the team win 14 of a maximum 18 points in the last six league games to finish in fifth place and secure a Europa League spot.
"Sascha Lewandowski and Sami Hyypia showed in the last six games that they can lead the team with a mix of competence, accuracy, charisma and composure," said club boss Wolfgang Holzhaeuser.
"This refreshing combination allows us to look towards our sporting future with a lot of optimism."
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