The left-handed ace joined his new team at Comerica Park before Saturday night's game against Colorado. He'll be part of a rotation that includes fellow AL Cy Young winners Max Scherzer and Justin Verlander.
Star slugger Miguel Cabrera and the division-leading Tigers have won three straight AL Central titles and hoping to win their first World Series title since 1984.
"Walking in the clubhouse today was like an All-Star Game. All the players I've seen over the years," Price said.
Price was 11-8 with a 3.11 ERA and topping the majors with 189 strikeouts when the Tigers got him from Tampa Bay on Thursday in a three-team trade that included Seattle. He'll make his first start for his new team Tuesday night at Yankee Stadium against New York.
The 28-year-old Price said he knew there was a good chance Tampa Bay would deal him before the trade deadline. His contract runs out after the 2015 season, and the fiscally challenged Rays probably wouldn't re-sign him.
Price said he was playing golf early Thursday when he got a text from Tigers reliever Joba Chamberlain that he could be headed to Detroit.
"I didn't know Detroit was in the running," Price recalled. He said his return text to Chamberlain simply said, "No way."
After golf, Price went to Tropicana Field for a workout. Then it was back home to wait by the phone with his girlfriend and his pet, a French bulldog named Astro.
Shortly before the 4 p.m. deadline, Price said his agent called and told him a deal would likely be made with Detroit and to be ready. About 15 minutes later, the call came that the deal had been finalized.
"It's very cool. To be able to sit here in the dugout and see what they do in the four days between starts," Price said.
With the Rays, Price was accustomed to heading the starters. With the Tigers, he's got plenty of talent around him.
"There's five leaders on this staff," Price said. "If Porcello is No. 5, that's pretty amazing the way he's thrown the ball."