Gourde, 26, will make an average of $5.17 million under the new deal, which runs through the 2024-25 season.
He has four goals and eight assists, tied for second on the team for points. He is also tied the team lead with three power-play goals and two game-winning goals.
"We are very pleased to have Yanni as a part of the Lightning organization for the foreseeable future," BriseBois said. "Yanni personifies our team's identity with his speed and relentlessness on the ice and his strong character off of it. He is proof of how far hard work and dedication can take you, and we look forward to him continuing his career in Tampa Bay."
For his career, Gourde has 35 goals and 85 points -- setting team rookie records in both categories last season. He also has 67 penalty minutes in 116 games.
The Associated Press contributed to this report.