Perez will receive a $500,000 buyout as part of a contract agreed to last winter that paid him a $3.5 million salary this year.
The 28-year-old was 10-7 with a 5.12 ERA in 29 starts and three relief appearances this year, striking out 135 and walking 67 in 165 1/3 innings. He is 53-56 with a 4.72 ERA in eight major league seasons that include 157 starts and 16 relief appearances.
Odorizzi, 29, was a career-best 15-7 with a 3.51 ERA and a career-high 178 strikeouts. He is 22-17 in two seasons since the Twins acquired him from Tampa Bay.
Minnesota also said Monday the New York Mets claimed left-hander Stephen Gonsalves off waivers. Minnesota right-hander Kohl Stewart refused an outright assignment to Triple-A Rochester and elected to become a free agent.
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