Reed, 24, saved 40 games in 48 chances last season with a 3.79 ERA and 72 strikeouts in 71 1/3 innings.
Davidson, 22, a former first-rounder who has been ranked among Baseball America's top 100 prospects, played at Triple-A Reno last season.
In 115 games for Reno, Davidson hit .280 with 32 doubles, 17 homers and 74 RBIs. In 31 games for the D-Backs, he hit .237 with six doubles, three homers and 12 RBI.
Free agent right-handed pitcher Gavin Floyd and the Atlanta Braves agreed on a one-year contract worth $4 million, multiple media outlets reported.
ESPN.com reported that Floyd could also receive up to an additional $4.5 million in incentives.
Floyd will be returning from Tommy John surgery and is not expected to be ready until May at the earliest.
Floyd, 30, made just five starts for the Chicago White Sox before undergoing surgery on May 6.
Players from the Japanese baseball league who want to play Major League Baseball will have greater choice in selecting the MLB team they play for based on the new protocols agreement between Major League Baseball and Nippon Professional Baseball (NPB).
In the past, there was no limit on the release fee MLB teams could pay to negotiate with a player who was playing in the NPB. Interested MLB teams simply submitted blind bids, and the highest bid then had exclusive negotiating rights for that player.
With the new agreement, however, NPB teams will set a release fee of no more than $20 million for a player.
Then, for a period of 30 days, any MLB team willing to pay the release fee can negotiate with the posted player.
The Houston Astros signed free agent reliever Matt Albers to a one-year, $2.45 million contract, FOXSports.com reported.
He had a 3.14 ERA in 63 innings for the Cleveland Indians in 2013.
Pitcher Shaun Marcum agreed to a minor-league deal with the Cleveland Indians, according to FoxSports.com. Marcum went 1-10 with a 5.19 ERA for the Mets in 2013 before being shut down to undergo thoracic outlet syndrome surgery.