Wood, 29, posted a 2.19 ERA with 21 saves in 54 appearances at Triple-A Indianapolis while in the Pirates organization last season. He struck out 67 and walked 23 in 70 innings, while being honored by Baseball America as the best reliever in the International League for a second straight year.
"My agent [Jonathan Maurer] and I had a game plan going in that we wanted the best opportunity for me," said Wood, who was courted by at least 10 other teams. "I didn't want to be that guy stuck in the Minors. I wanted an ample opportunity to make the team, and Minnesota offered that opportunity."
The 6-foot right-hander last appeared in the Majors in 2011, when he had a 5.63 ERA in eight innings with the Pirates. He also had 23 saves and a 2.84 ERA in 40 appearances at Indianapolis that season.
Wood said he's looking forward to competing for a spot in the bullpen in Spring Training, as he's hoping to crack an Opening Day roster for the first time since he did it with the Marlins in '10.
"That's the goal going into camp," Wood said. "I've been at Triple-A the past two years and have done pretty well, so I feel like if I get the opportunity I can go out there and get Major League hitters out."
Wood has a career 4.50 ERA in 57 big league appearances. His best season came in 2009 with the Marlins, when he had a 2.82 ERA in 22 1/3 innings.
Wood is mostly a fastball/slider pitcher, with his fastball coming in at 94-98 mph and his slider at 89-91 mph.
He was originally drafted by the Marlins in the 44th round of the 2002 First-Year Player Draft out of Pima Community College in his hometown of Tucson, Ariz.
Fryer, meanwhile, played in six games with the Pirates last season, going 1-for-4 with a walk. He also hit .204/.257/.247 with no homers and 10 RBIs in 65 games at Triple-A Indianapolis.
Fryer, 27, is a career .273/.361/.409 hitter in the Minors, and was originally drafted by the Brewers in the 10th round of the 2007 Draft.
Fryer and Wood played together in Triple-A the last two seasons, and Wood pointed out Fryer adds some versatility because of his ability to play the outfield as well as catch.
"He's a guy you can trust behind the plate," Wood said. "He calls a good game and we've been on the same page for the last couple years. So it's nice to sign with the Twins and have a familiar face around, too."