The Twins and the cash-strapped Tampa Bay Rays had plenty of trade conversations throughout the offseason. Saturday evening, all those cell minutes and text messages finally bore fruit. Right-hander Jake Odorizzi, who turns 28 just before Opening Day, will make the short drive from Port Charlotte, Fla., to Fort Myers to join his new team. In exchange for Odorizzi, who won his arbitration hearing this week and will make $6.3 million this season, the Twins gave up only Class A shortstop Jermaine Palacios. Though coming off an injury-marred season that included a 4.14 earned run average and a 10-8 record in 28 starts, Odorizzi becomes the leading contender to start on Opening Day in place of Ervin Santana, who could miss the first month after finger surgery on his pitching hand. Odorizzi left his final start of 2017 for precautionary reasons with a sore right knee and also had stints on the disabled list due to a lower back strain (July) and a strained left hamstring (April). A 2008 first-round pick of the Milwaukee Brewers out of high school in New Douglas, Ill., Odorizzi has now been traded three times. He also headed to the Kansas City Royals as part of the package for Zack Greinke in 2010 and was dealt to the Rays in 2012 as part of the haul for Wade Davis and James Shields. Odorizzi has one more year of arbitration eligibility before his first possible crack at free agency. Factoring in a theoretical 50-percent raise for 2019, he should be under Twins’ control for around $16 million over the next two seasons. By comparison, they spent $16.75 million last month for two years of setup reliever Addison Reed on a strangely frozen free-agent market.