The 28-year-old Santiago, an All-Star last season, was 10-4 with a 4.25 ERA in 22 starts for the Angels while making $5 million this year. He will be eligible for free agency after the 2017 season.
The 33-year-old Nolasco went 15-22 with a 5.44 ERA for the Twins after signing a $49 million, four-year contract before the 2014 season.
Meyer, 26, was acquired prior to the 2013 season from Washington for center fielder Denard Span. He was 0-1 with a 12.27 ERA in two appearances (one start) for the Twins this season.
Busenitz, 25, the Angels' 25th-round pick in the 2013 draft, was 0-2 with a 3.55 ERA in 24 appearances for two clubs in the Angels' minor league system.
The Associated Press contributed to this report.