Curtiss pitched in 17 games for the Twins over the past two seasons, going 0-1 with a 7.20 ERA in 15 innings. He walked six and struck out 17. The right-hander was designated for assignment Monday to make room for pitcher Blake Parker.
The 18-year-old Ozoria played for two rookie-level teams last season, batting a combined .195 with 12 RBI in 51 games.
Minnesota announced the deal Tuesday night.