Reddick, 26, is entering the arbitration process for the first time and is coming off a season in which he batted .226 with 12 home runs and 56 RBIs in 114 games while dealing with a wrist injury much of the year. He hit 32 homers and 85 RBIs with a .242 average and won an American League Gold Glove Award while playing 156 games in 2012.
No contract terms were released by the A's, but Joel Sherman of the New York Post reported that Lowrie signed for $5.25 million, Gregerson for $5.065 million, Moss for $4.1 million and Gentry for $1.45 million.
The A's also avoided arbitration with newly acquired closer Jim Johnson and catcher/designated hitter John Jaso by inking them to one-year deals on Thursday, with Johnson signing for $10 million and Jaso for $2.3 million.
Lowrie, in his final year of arbitration eligibility, earned the biggest pay increase of Friday's four signees. The 29-year-old infielder made $2.4 million in 2013 in his first season with the A's while batting .290 with 45 doubles, 15 home runs and 75 RBIs in 154 games. Lowrie played 119 games at shortstop, 24 at second base and 13 at designated hitter.
He set an A's record for doubles by a switch-hitter and an Oakland record for hits by a switch-hitter (175), while tying the Oakland record for batting average by a switch-hitter. The 45 doubles ranked second in the American League, second in Oakland history and tied for seventh in Athletics history.
Gregerson, 29, is also in his final year of arbitration eligibility after earning $3.2 million last year with San Diego. The 6-foot-3 southpaw was 6-8 with four saves and a 2.71 ERA in 73 appearances in 2013, recording 64 strikeouts in 66 1/3 innings while posting a 1.010 WHIP.
Gregerson has a career ERA of 2.88 in five seasons with the Padres and has struck out 352 batters in 347 innings. He topped 70 games for the fourth time in the last five years in 2013, and his 363 appearances since 2009 are the most in the Majors in that span. Like Lowrie, he'll be a free agent following this season.
Moss, 30, made $1.6 million last year in his first year of arbitration eligibility as a Super Two qualifier. He batted .256 and posted career highs with 30 home runs and 87 RBIs in 145 games. Moss ranked sixth in the AL in slugging percentage at .522 and 10th in OPS at .859.
Moss was used mostly in a platoon role against right-handed pitchers, but he still tied for eighth in the AL in home runs. He was fourth in the league in fewest at-bats per home run (14.9) and fifth in fewest at-bats per RBI (5.1). He's posted a .269 average with 51 home runs and 139 RBIs in 229 games in two seasons with the A's.
Gentry, acquired by trade from Texas this offseason, signed for $1.145 million in his first year of arbitration. The 30-year-old outfielder hit .280 with two home runs, 22 RBIs and 24 stolen bases last year in 106 games for the Rangers.
Gentry's 88.9 percent success rate on stolen bases (24-of-27) was the third-best percentage in the AL, and he's now 56-for-66 (84.5 percent) in his career. Gentry hit .338 with a .428 on-base percentage in 55 games after the All-Star break.