Hjulmand moves to the Bundesliga outfit from Nordsjaelland having guided the club to their first Danish Superliga title in 2012, leading to UEFA Champions League football the following season.
The 42-year-old has agreed a three-year contract at the Coface Arena that will see him remain in charge until 2017.
Managing director Christian Heidel was delighted to welcome the Dane and is confident he can continue the good work done by Tuchel, who stood down on Sunday after guiding the club into the Europa League.
"Kasper Hjulmand fits into the profile created by us in our search for a new coach," Heidel told Mainz's official website. "He has very high level of expertise, he is a meticulous trainer and advocate of attacking football style.
"He has an excellent reputation as a developer and trainer of young players. We are very pleased that we have managed to inspire him for us."
Hjulmand is relishing the new challenge in front of him as he looks to push the club on from their seventh-place finish in the Bundesliga this season.
"When I decided to leave FC Nordsjaelland and seek a new job, I wanted to wait for the right club for me and take me for finding time," he said. "Then came the request of Mainz, I have followed the Bundesliga and had already an idea of the club.
"In talks with Christian Heidel I was surprised at how perfectly the philosophy of the club suits my personal.
"For me, the move to Mainz 05 is a decision of the heart."
