It was reported that the swingman had signed a four-year offer sheet from the Hornets worth $63m (£36.8m) earlier this week, which the Jazz had three days to match.
Mark Bartelstein told ESPN: "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.
"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 organisation 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."
Hayward averaged a career-high 16.2 points per game during the 2013-14 regular season.