Both players were released by the club Thursday after clearing waivers.
Wright was designated for assignment last week when the Indians recalled right-hander Frank Herrmann. Grudzielanek was designated for assignment on Tuesday to make room for infielder Anderson Hernandez.
Wright went 1-2 with a 5.48 ERA in 18 games.
The 39-year-old Grudzielanek batted .273 with 11 RBIs. He injured his hamstring last weekend and was given the option of going on the 60-day disabled list. He chose not to so he could sign elsewhere.