Gray had a 3.08 ERA in 24 starts after arriving in a trade with Cincinnati that sent 2021 first-round draft pick Chase Petty to the Reds. Gray had 117 strikeouts in 119⅔ innings.
They have the following buyouts: $750,000 for Archer, $1 million for Bundy and $2.75 million for Sano.
The 29-year-old Sano faded hard into a quiet and disappointing ending with the Twins, who signed him at age 16 out of the Dominican Republic in 2009. Since his debut in 2015, no major league player struck out more than Sano, with 1,042 in 694 games.
After making the All-Star team in 2017, Sano batted just .217 over the past five seasons. He had trouble staying healthy throughout his tenure with the Twins, including a knee injury this year that limited him to 20 games. He had five hits in 60 at-bats.
Bundy led the Twins with 29 starts, posting a 4.89 ERA over 140 innings. Archer had a 4.56 ERA in 102⅔ innings, making 25 starts for his most since 2018 after thoracic outlet syndrome wrecked his previous two seasons.
The Associated Press contributed to this report.