Davis led the majors last season with 53 home runs and 138 RBIs, both career highs. He earned $3.3 million.
The 27-year-old Davis played in 160 games, batted .286, had 167 hits and scored 103 runs.
Hunter was 6-5 with a 2.81 ERA in a career-high 68 games for the Orioles last year. He will earn $3 million in 2014, a solid increase from the $1.82 million he received last season.
After coming to Baltimore in a trade with Houston, Norris went 4-3 in 11 games. The right-hander agreed to terms on a $5.3 million contract.
Matusz and Patton, both left-handers, pitched out of the bullpen. Matusz will earn $2.4 million in 2014 after receiving $1.6 million last season, and Patton will receive $1,275,000 next season, up from $825,000 in 2013.
The Orioles have exchanged arbitration figures with catcher Matt Wieters, offering $6.5 million while he's seeking $8.75 million.