The Predators, who have not won a playoff series since 2018, also added former Carolina defenseman Brady Skjei as dealmaking began for the 2024-25 campaign.
Stamkos, who won two Stanley Cup titles and spent his entire 16-year NHL career with the Tampa Bay Lightning, signed a four-year deal worth $32 million with the Preds.
The Lightning, who parted ways with their 34-year-old captain after landing Carolina's Jake Guentzel for seven years at $63 million on Monday, got 40 goals and 41 assists from Stamkos last season.
"Thank you, Tampa. I don't have the words yet ... I will soon," Stamkos posted on social media.
"It's still too early to process. Just wanted everyone to know how thankful we are for 16 years as a Bolt. My family and I are excited for the next chapter."
Joining him in Nashville will be 33-year-old right wing Marchessault, who left for a five-year deal worth $27.5 million. He was the Conn Smythe Trophy winner as the Most Valuable Player in the Vegas Golden Knights' run to the Stanley Cup in 2023.
Marchessault spent parts of two seasons in Tampa Bay and another in Florida before becoming an original member of the Golden Knights. He has 230 goals and 257 assist in 638 NHL career contests.
Skjei will get $49 million over seven seasons to try and help spark the Predators, who went 47-30 with five overtime losses last season before being ousted by Vancouver in the first round of the playoffs.
Nashville has not reached the Stanley Cup Final since 2017, when the Predators lost to Pittsburgh in six games.
