Kampl, a product of Leverkusen's youth teams, made his Bundesliga debut with Borussia Dortmund midway through the 2014/15 season after an earlier move to Leipzig fell through.
He had previously played for Leipzig's sister team RB Salzburg. Both teams are owned by energy drinks maker Red Bull.
No financial details of the four-year contract were made public. It is reportedly worth up to 20 million euros including bonus payments.
Leipzig, promoted to the top division last season, unexpectedly finished runners-up to champions Bayern Munich and will compete in the Champions League group stage.
(Reporting by Karolos Grohmann; editing by John Stonestreet)
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