The 22-year-old's deal carries an annual average value of $4.45 million, according to reports.
"We are very pleased to sign Christian to a long-term contract," Coyotes general manager John Chayka said in a statement. "Christian is a highly skilled, reliable, two-way center who continues to improve each season. He will be a key player for us in the future and we are thrilled to have him with us for the next seven seasons."
The Coyotes have had a busy offseason, signing defensive star Oliver Ekman-Larsson to an eight-year contract, giving defenseman Niklas Hjalmarsson a two-year extension and signing forward Michael Grabner to a three-year deal.
"I am very happy to sign a long-term contract with the Coyotes," Dvorak said in a statement. "We have a great young team with a bright future and I love living and playing in the Valley. I'm excited to be a Coyote for the next seven years."