The 28-year-old midfielder becomes Oliver Glasner's first signing since taking charge at the Premier League club, with the pair linking up again after previously working together at VfL Wolfsburg.
Schlager arrives after making 30 appearances in all competitions for Leipzig last season, scoring three goals while also serving as the club's vice-captain.
The experienced midfielder has earned 55 caps for Austria and started all four of his country's matches at the World Cup.
Speaking after completing the move, Schlager said Forest's ambitions played a major role in his decision to join the club.
"The club has big ambitions and so do I," he said.
"I want to be back in European competitions and we have a good chance of achieving that. It is the best feeling to play international football during the week, and I want to experience that again."
Aston Villa have completed the signing of Argentina winger Alejandro Garnacho from Chelsea on a season-long loan, with a conditional obligation to make the move permanent next year.
Arsenal have completed the signing of Greek winger Christos Tzolis as Mikel Arteta continues to strengthen his squad ahead of the new season.
Barcelona have confirmed the signing of Germany international Karim Adeyemi from Borussia Dortmund on a five-year contract, with the winger completing a move he described as a childhood dream.
Tottenham Hotspur goalkeeper Guglielmo Vicario has been omitted from the pre-season tour squad of New Zealand and Australia, with Lucas Bergvall included.
