The Lightning signed the unrestricted free agent to a seven-year,
$31.5 million contract, ESPN.com has confirmed.
Tampa Bay dealt a third-round draft pick in 2009 for the short-term negotiating rights to Malone and Pittsburgh Penguins teammate Gary Roberts on Saturday. That allowed the Lightning to talk exclusively to Malone until the NHL's free agency signing period begins Tuesday.
The Penguins didn't feel they could afford to re-sign Malone, who had 27 goals and 24 assists last season. The Pittsburgh native was believed to be seeking about $5 million per season.
Malone has 87 goals and 82 assists in 299 career games, all with the Penguins.
The Wild will get a selection in either the 2009 or 2010 draft. Wild spokesman Aaron Sickman said Sunday night it will depend on whether Tampa Bay re-signs Rolston.
Wild general manager Doug Risebrough said recently that if a deal wasn't reached by Tuesday, it likely would signal the end of Rolston's days in Minnesota.
Minnesota had been hoping to retain the 35-year-old Rolston for a few more years after getting 96 goals and 106 assists from him the past three seasons.
Rolston had been one of Minnesota's most consistent and reliable players, missing only five games during his first three seasons with the Wild.
Rolston, who hit the 30-goal mark three consecutive seasons for the Wild, sent text messages to Twin Cities newspapers earlier Sunday saying he was "going to the first of July." He did not elaborate, and it wasn't immediately clear Sunday night whether he still planned to become a free agent Tuesday or whether he would try to reach a deal with Tampa Bay.
Information from The Associated Press contributed to this report.