Willingham, 35, played nearly three seasons with the Twins after signing a three-year, $21 million deal before the 2012 season. He hit .232/.353/.446 with 61 homers and 192 RBIs in 324 games with Minnesota before being traded.
Willingham said he enjoyed his time with the Twins despite their struggles, but he was excited to join a club in the thick of the playoff race.
"It was strange because the first couple days, you don't really know the guys so you're just trying to fit in," Willingham said. "But there's a lot of good energy here and lots of really good players, too. A lot of good things are happening. We're getting good pitching and timely hitting. So I'm looking forward to what's to come."
Willingham, who has played in the big leagues for 11 years, has never played in the postseason. So he's looking forward to trying to help the Royals down the stretch as they aim for their first playoff berth since 1985.
"It would mean a lot," Willingham said. "Playing games that mean something in August and September, I've never experienced that before. So I'm glad I'm able to experience that this year. I just want to help my ballclub get to October."
Twins manager Ron Gardenhire, who informed Willingham of the trade shortly before Monday's game against the Astros, said Willingham's presence is missed.
"He's a guy who can put the ball in the seats," Gardenhire said. "He was actually swinging pretty good as of late for us, driving the baseball. But he's a class act and a leader. He's a quiet guy but does really well with the kids. He's one of those guys we hated to see leave."
Rhett Bollinger is a reporter for MLB.com. Read his blog, Bollinger Beat, and follow him on Twitter @RhettBollinger. This story was not subject to the approval of Major League Baseball or its clubs.