The Dodgers also designated pitcher Jarret Martin for assignment.
Brigham has yet to make his MLB debut.
Cody Hall , Joan Gregorio and Ray Black all had their contracts purchased. All three players are protected from being selected in the Rule 5 draft. In order to make room on the 40-man roster, the team designated J.C. Gutierrez for assignment.
Goforth posted a 3.76 ERA in 64 2/3 innings at Double-A last season. The 26-year-old will be inelligible for the Rule 5 draft following the move.
Jameson Taillon , Nick Kingham , Willy Garcia and Elias Diaz all had their contracts purchased. In order to make room on the 40-man roster, the team outrighted Brent Morel and designated Ramon Cabrera for assignment.
Edwards is considered one of the team's best pitching prospects. The 23-year-old posted a 2.35 ERA over two levels in 2014.
Waldrop is a former first round draft pick with the Twins. Garrett posted a 3.64 ERA over 133 1/3 innings at Class A.
The team purchased the contract of pitcher Kevin Munson and A.J. Schugel . Both players are now unavailable for the Rule-5 draft. In order to make room on the roster, the team designated Mike Bolsinger and Charles Brewer for assignment.
Pitcher Jeff Walters, who's recovering from Tommy John surgery, was removed from the 40-man roster.