The Germany international joins the Reds for a British record fee, with the final terms settled at £116m.
The £16m in bonuses is dependent on appearances and success, including the Premier League and Champions League titles.
The move still falls short of Bayer's initial €150m (pound;127m) demands, though the Germans did reduce their price after seeing Manchester City and Bayern Munich drop out of the race due to the valuation.
The current British record was the £115m Chelsea paid Brighton two years ago for Moises Caicedo - a fee Liverpool could've paid if the Ecuador international had agreed to move to Anfield at the time.
Wirtz was set to undergo a medical at Liverpool this week, but as talks dragged on he chose to go on holiday. As such, his tests are expected to be conducted once his summer break concludes.