The Pirates expect Resop to arrive in time for Thursday's night game against the Rockies. Steven Jackson was designated for assignment to open up a spot for Resop on both the 40- and 25-man rosters.
Park, who was designated for assignment by the Yankees on Saturday, won't be added to the roster until Friday. Space was made for him on the 40-man roster by transferring Steve Pearce to the 60-day disabled list.
The Pirates will have to remove another reliever off the 25-man roster upon Park's arrival on Friday.
Resop has made only one Major League appearance since 2008, that coming with Atlanta on June 15. He allowed five earned runs on five hits and three walks in two innings. The next day, the righty was placed on the disabled list with a strained left oblique muscle.
He has spent the rest of the season in the Minors as a starter. With Triple-A Gwinnett (Ga.), he went 6-3 with a 2.09 ERA in 15 starts. The 27-year-old pitched in Japan in 2009 and has accumulated 63 big league innings since making his debut in 2005.
"Adding Resop should help us," manager John Russell said. "He's been doing very well. He has shown some good numbers and hopefully he'll be a guy who can come in and help us out."
Park, a 17-year veteran, appeared in 29 games for the Yankees this season. He allowed 22 earned runs on 40 hits and 12 walks in 35 1/3 innings. Park also struck out 29.
The Pirates will be the seventh different team the 37-year-old South Korea native has played for since making his Major League debut in 1994. The Pirates will be responsible for paying what remains on Park's $1.2 million contract. He will be a free agent after the season.
Wednesday's two acquisitions come after a 9-4 loss to Cincinnati that showcased how badly the Pirates need help in their bullpen. The club lost four veteran bullpen members in the last week and a half.