Mark Bartelstein, Hayward's agent, told ESPN.com that the Jazz made "a great statement" to his client by matching the Hornets' offer.
Hayward will make $14.7 million this season and will have a player option heading into the final year of the pact in 2017-18.
After passing his physical, Hayward tweeted, "Officially back with the @utahjazz!!!! Wanna thank them and all of #jazznation for believing in me! Lots of work ahead...
"We're extremely appreciative to Michael Jordan, Rich Cho, Steve Clifford and the Hornets for wanting Gordon and making Gordon feel like such a critical piece to the team they're building," Bartelstein said. "That's something that's really appreciated by Gordon and myself, not just the contract but the whole presentation that they made.
"But It's always a wonderful thing when your own organization values you so much that they'd match a contract like this. I think it makes a great statement to Gordon about how they feel about him and value him."
The Jazz previously had stated over the past several months that they intended to match any offers for the 24-year-old Hayward, who averaged career highs of 16.2 points, 5.1 rebounds and 5.2 assists last season.
The Jazz could have kept Hayward off the open market had they negotiated a contract extension with the versatile swingman back in October.
But talks broke down last year, with Hayward reportedly seeking a four-year contract valued at $13 million annually and Utah reportedly holding firm at $12 million annually.
The Jazz will continue to make Hayward a centerpiece of the organization, rebuilding around young players like Derrick Favors, Trey Burke, Alec Burks, Enes Kanter, Dante Exum and Rodney Hood.