In a statement, the family said they remembered her "bright smile [and] positivity".
Combs, 39, had been dubbed the "fastest woman on four wheels".
She earned the title in 2013 when she reached 398 miles per hour (641km/h). Combs was trying to best that speed and the absolute women's land speed record of 512 miles per hour (824km/h) - set by Kitty O'Neil in 1976 - when she crashed.
"Jessi's most notable dream was to become the fastest woman on Earth, a dream she had been chasing since 2012... and she left this Earth driving faster than any other woman in history," her family said.
Her teammate Terry Madden also paid tribute to her on social media.
"Unfortunately we lost her yesterday in a horrific accident, I was the first one there and trust me we did everything humanly possible to save her," he said in an Instagram post on Wednesday.
Combs had appeared on a number of television shows, including Overhaulin', All Girls Garage and Mythbusters.
She was a driver with the North American Eagle Supersonic Speed Challenger team and had been chronicling her attempt to set a new land-speed record in the days before her death.
"It may seem a little crazy to walk directly into the line of fire... those who are willing, are those who achieve great things. People say I'm crazy. I say thank you," she wrote on Instagram this week.
https://www.bbc.com/news/world-us-canada-49504222