Staal, a 35-year-old center, scored 47 points (19 goals, 28 assists) in 66 games with the Wild this season and five points (one goal, four assists) in four games in the Stanley Cup Qualifiers.
"The way [the trade] happened was a bit out of the blue, [a shock] for me and my family, but that's sports, that's how some things go," Staal said. "And we'll figure out and navigate as we go. Hopefully I can be impactful. That's the plan."
Staal has one season remaining on a two-year contract worth $3.25 million annually he signed with Minnesota on Feb. 25, 2019.
"Eric Staal was a positive influence on guys, but sometimes it's just change is good for us," Wild general manager Bill Guerin said. "This is part of it. We need to mix things up. We need to find a different pathway to success, and that's what we're trying to do. We're trying to build a better team, and sometimes you have to take some drastic measures.
"We're getting a little bit younger. It's a different look for our team. Marcus provides a lot of speed, a lot of skill, and we're looking forward to adding him to our lineup."
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Selected by the Carolina Hurricanes with the No. 2 pick in the 2003 NHL Draft, Staal has scored 1,021 points (436 goals, 585 assists) in 1,240 games with the Hurricanes, New York Rangers and Wild, and 51 points (21 goals, 30 points) in 62 Stanley Cup Playoff games. He has scored at least 40 goals three times in the NHL, including in 2005-06, when he scored an NHL career-high 100 points (45 goals, 55 assists) to help Carolina win its first Stanley Cup championship.
"Eric Staal has had a world-class career. He's won a Stanley Cup, he's won an Olympic gold medal, he's won a World Championship gold medal, he's been an all-star many times, he's still a productive player," said Sabres general manager Kevyn Adams, who won the Stanley Cup with Staal in 2006. "What I'm telling you there is just what's on the ice. He's a tremendous person, high character, former captain. Obviously in the past with my having been a teammate with him, I've seen it up close and personal. We've added a phenomenal player and person, and I'm very excited about it."
Buffalo is hoping Staal can provide depth at center behind Jack Eichel, who scored 78 points (36 goals, 42 assists) in 68 games this season. Staal played with Sabres left wing Jeff Skinner on the Hurricanes from 2010-16, so there's a chance their chemistry could help Skinner bounce back after he dipped to 14 goals last season after he scored 40 in 2018-19.
"I know [the Sabres] have a lot of talent," Staal said. "I know Jack is elite. There's also [Skinner] who I played with in Carolina. There are great players there who are competitive. For me, I'm just going to try to be myself coming in, and hopefully as a group we can develop that team atmosphere, the desire to win and compete every night."
Johansson, a 29-year-old forward, scored 30 points (nine goals, 21 assists) in 60 games in his only season with Buffalo. He has one season remaining on a two-year contract worth $4.5 million annually he signed July 6, 2019.
Selected by the Washington Capitals in the first round (No. 24) of the 2009 NHL Draft, Johansson has scored 364 points (129 goals, 235 assists) in 648 games with the Capitals, New Jersey Devils, Boston Bruins and Sabres. He scored 41 points (13 goals, 28 assists) in 94 playoff games.
"I had no idea this was going on and it's always weird when this stuff happens and you don't see it coming, but I'm very happy. ... I can't wait to get to Minnesota," Johansson said Thursday. "I know (defenseman) Jonas Brodin and (center) Joel Eriksson Ek very well and looking forward to playing with them. They only have good things to say about Minnesota and the organization and everything, so I'm looking forward to it a lot."
Johansson said he anticipates moving back to center.
"I grew up a centerman and kind of always had been playing that position," he said, "but for the last years I've been a wing full-time, basically. It took a little bit to get used to it, but I like playing center. It's like you get involved a lot. You get to play with the puck a lot too, which I like. I'm up to playing whatever they want me to play and just looking forward to doing it."
Guerin explained why he believes Johannson will have success there with Minnesota.
"I think opportunity," Guerin said. "They've got a pretty good No. 1 centerman [in Buffalo] (Eichel), and sometimes it's not a great fit, but I think Marcus fits well with us and he's going to get a lot opportunity. (Coach) Dean [Evason] knows him very well from Washington (as a former assistant) and believes he can an impactful centerman, so he's going to get that opportunity."
NHL.com staff writers Tom Gulitti and Mike Zeisberger contributed to this report
Video: Wild acquire Staal for Johansson