Ristolainen signed a six-year $32.4 million contract, while Kucherov signed a three-year deal that averages $4.766 million a year. Both were restricted free agents whose rights were retained by their respective teams in June.
For Buffalo, the signing means the Sabres will have their top defenseman ready for their opener against Montreal on Thursday.
The Lightning, meanwhile, have their nucleus intact in preparing to open their season by hosting Detroit on Thursday. Kucherov led the Lightning with 30 goals and 66 points in the regular season, and led them again in the playoffs with 11 goals and 19 points.
Their signings left three prominent restricted free agents still without contracts, including Winnipeg defenseman Jacob Trouba, who has asked to be traded. Also unsigned are Anaheim Ducks defenseman Hampus Lindholm and forward Rickard Rakell.
In another move Tuesday, veteran forward Pierre-Alexandre Parenteau was claimed by the New Jersey Devils a day after being placed on waivers by the New York Islanders. Parenteau is a two-time 20-goal scorer, who is joining his eighth team in nine NHL seasons. New Jersey freed up roster space by placing defenseman Seth Helgeson on waivers.
- Ruslan Fedotenko announced he is retiring after 12 NHL seasons split among five teams. Fedotenko is a two-time Stanley Cup champion who spent the past two seasons playing for Iowa of the American Hockey League. He had 173 goals and 193 assists for 366 points in 863 NHL games.
- Los Angeles kept forward Devin Setoguchi. The veteran played his way onto the roster after nearly two years out of the NHL, during which he dealt with an alcohol problem. The Kings also sent veteran defenseman Rob Scuderi, a two-time Stanley Cup champion, to the minors after he cleared waivers.
- Calgary signed free-agent forward Kris Versteeg to a one-year contract. Versteeg is a nine-year NHL veteran and a two-time Stanley Cup champion, who split last season with Carolina and Los Angeles.
- Pittsburgh claimed Montreal goalie Mike Condon; Minnesota claimed Detroit forward Teemu Pulkkinen; Toronto claimed Boston forward Seth Griffith; and Carolina claimed Phoenix defenseman Klas Dahlbeck.
- The New York Rangers placed forward Nathan Gerbe on waivers with the intention of terminating his contract.
- The Hurricanes acquired forward Connor Brickley from the Florida Panthers for forward Brody Sutter in a swap of prospects. Sutter is the 25-year-old son of former Panthers coach Duane Sutter and had no points in 12 games over two seasons with the Hurricanes.