Radke, 27, agreed on Monday to a new four-year contract worth a reported $36 million and containing an opt-out clause after 2001 and a no-trade provision for the final three years.
The deal is the richest in team history, with the right-hander's annual salary of about $9 million surpassing Kirby Puckett's highest salary of $7 million in 1996.
"This is just the beginning of good things to happen," Radke said before the Twins played the Red Sox. "This team has a lot of potential."
The Twins have the lowest payroll in baseball this year, $16.5 million. They are in last place in the American League Central and the last time they finished higher than fourth was in 1992, when the Twins ended the season in second place.
Still, optimism abounded in the Metrodome after Radke discussed his new contract.
"This is one player we needed to keep," general manager Terry Ryan said. "It's our responsibility to move forward and improve this franchise."
Manager Tom Kelly, who sat in the dugout and watched reporters and cameras surround Radke, said he felt cautiously optimistic about the Twins' future.
"This is a good building block for the Twins and the organization," he said.
Radke is 5-9 this season with a 3.95 ERA in 18 starts. His career mark is 71-77 with a 4.26 ERA. His best season was in 1997, when he went 20-10 with a 3.87 ERA and became one of three pitchers in the last 50 years to win 12 straight decisions.
Neither Radke nor team officials would confirm the salary amount, but they did confirm the contract would allow Radke to demand a trade after 2001. Radke and his agent, Ron Simon, had been insisting on such an opt-out provision.
Radke, who would have been eligible for free agency after this season, said he would carefully weigh his options after next season before considering whether to demand a trade.
"I just want to see what happens after the first year and in the offseason," he said.
Radke also said the opt-out clause was one of the clinchers in persuading him and Simon to agree to a deal, even though Simon cut off negotiations with the Twins in February.
"They tried really hard to sign me and I'm just overwhelmed with what I have," he said.
Ryan said he's confident Radke won't demand to be traded because the pitcher has been loyal to the Twins, and Ryan is confident the Twins are on a new path toward becoming a contender in a few years.
"It's not something that I'm overly concerned about as long as the organization continues to move forward," Ran said. "This was just the first step."
Radke also credited Twins new CEO Chris Clouser, hired last month for the newly created position.
Ryan had been held back by owner Carl Pohlad's desire to keep the payroll down. Ryan said he hadn't received any specifics about whether the purse strings would be loosened, but said Radke's signing was a good indicator.
"I don't know exactly where that payroll's going, but this gives us hope," Ryan said.