Right-hander Karstens went 9-9 with a 3.38 earned run average in 30 games (26 starts) this past season. He is 21-36 with a 4.52 ERA in 119 games (76 starts) for his career.
Sources indicated the 29-year-old hurler will be paid $3.1 million. He worked under a $1.1 million contract in 2011.
Meek endured a forgettable 2011 campaign as injuries limited him to only 24 games.
The 28-year-old right-hander was coming off an All-Star season in which he posted a 2.14 earned run average in a career-high 70 appearances.
For his career, Meek has compiled a 7-7 record with four saves and a 3.08 ERA in 144 games, all with the Pirates.
Meek is slated to earn $875,000 with the chance to make an additional $25,000 in performance-based incentives.
Garrett Jones and Casey McGehee did not agree to terms and will head to arbitration. Each side has submitted a desired salary figure.