Tampa Bay will also send a seventh-round pick to the Sharks.
The trade was announced minutes before the teams met at the Tampa Bay Times Forum; Moore was not in the lineup.
"Dominic is an extremely versatile player that has performed in a lot of important playoff games the last two years," Sharks general manager Doug Wilson said in a statement. "We feel that he is a great fit in several areas and his veteran presence will benefit our team greatly."
SOG: 74 | +/-: -10
“One of our assistants, Matt Shaw, had him in Minnesota and they were really happy with him there," Sharks coach Todd McLellan said after the game, a 6-5 overtime win by the Lightning. "He can play all over the board. He can check, penalty kill and he’s good in the faceoff circle. It sounds like he’s got some very strong character to him, and I think he’ll fit in very well with our club.”
Moore also had three goals and 11 points in 18 games for the Lightning in last spring's Stanley Cup Playoffs.
"He’s going to help us," Sharks center Logan Couture said. "He’s got some grit. He was big for them in the playoffs last year during their playoff run. So, he’s going to help our team. I haven’t met him yet, but he’s definitely going to help us.”
"We're not looking to get rid of guys," he said. "Our feeling was that if we had good offers we would act on it. Getting a second-round pick is very valuable for us. It came together very quickly but it was not something we worked on for a long time."
"I really have nothing else in the works right now -- obviously, Pavel Kubina's situation but we'll take it one day at a time.”
The Lightning scratched veteran defenseman Kubina for Thursday's game and have asked him to which teams he would accept a trade.
Tampa Bay now owns three selections in the second round of the draft -- the Lightning also acquired Philadelphia's second-round choice on July 1, 2010, in exchange for defenseman Andrej Meszaros.
Yzerman said getting a second-rounder for Moore was too good a deal to pass up.
"We debated. He is a good player, a real leader a good citizen," he said. "We just felt like it was a high pick that was too valuable to pass up."