In return, the Twins will get Alex Presley and either cash or a player to be named later.
Morneau has an average of .259 with 17 home runs and 74 RBIs this season with Minnesota.
The 32-year-old native of New Westminster, B.C., was placed on waivers August 13 by the Twins and will join a Pirate team tied for the NL Central lead with the St. Louis Cardinals.
Morneau, who won the American League MVP award in 2006, has been with the Twins for the past 11 seasons.
Pittsburgh continues to stack its roster ahead of a possible playoff run. The team acquired outfielder Marlon Byrd and catcher John Buck from the Mets four days ago.