Tonkin had his contract selected by the Twins on Tuesday.
Tonkin will rejoin the big club after being designated for assignment by the Twins back in May. He posted an impressive 1.73 ERA and 61:13 K:BB through 41.2 innings with Triple-A Rochester, but his 6.55 ERA across 11 big-league innings this season will likely limit his opportunities to lower-leveraging situations. J.T. Chargois (elbow) was shifted to the 60-day disabled list to open up a spot on the 40-man roster for Tonkin.