The team announced that it has signed the defenseman to a one-year, $1.75 million contract.
The Rangers bought out the last two years of Shattenkirk's contract last week.
Shattenkirk said he chose the Lightning from among six or seven NHL teams interested in signing him and compared his situation after the buyout to theirs after losing in the first round of the playoffs.
"I think I have a huge chip on my shoulder right now,'' Shattenkirk said on a conference call. "I want to show I'm back to my old self and prove that I can be a player in this league again.''
Shattenkirk, 30, played 119 games with the Rangers over the past two seasons, scoring 51 points (7 goals, 44 assists) with a minus-29. But his game never recovered after an injury-filled first season with the team, and his 1.4 shooting percentage last season was the worst of his career.
"After a full summer of training when he's healthy and he feels confident in his leg, we expect him to be a strong contributor for our team this coming season,'' Lightning vice president and general manager Julien BriseBois said.
His contract carried an average annual value against the salary cap of $6.65 million through 2021. According to Cap Friendly, the Rangers will save $5,166,667 against the cap this season, as Shattenkirk's cap hit would be reduced to $1,483,333 in 2019-20.
The buyout will be spread out over the next four seasons, with the Rangers also paying him $6,083,333 in 2020-21 and $1,433,333 in 2021-22 and 2022-23.
After a year splitting time with the St. Louis Blues and Washington Capitals, Shattenkirk became a coveted unrestricted free agent in the summer of 2017 as one of the NHL's better puck-moving defensemen. Spurning longer-term deals, on July 1, 2017, he signed a four-year, $26 million contract with the Rangers, his favorite team as a child while growing up in New Rochelle, New York, where his parents still live.
He said he doesn't regret signing with his hometown Rangers. He said he was ticked off to be bought out but also about the Rangers' move toward a rebuild and his own play.
"It's definitely not a success story,'' Shattenkirk said. "A lot of these things, they have to be learning experiences.''
ESPN's Greg Wyshynski and The Associated Press contributed to this report.