Anderson, a dominant closer for the University of Florida, will get a chance to start in the Red Sox's farm system.
Gorst is a power righty out of Georgia Tech who was one of the nation's best closers in 2016.
The Red Sox have signed six of their top nine picks, but haven't reached a deal with Jason Grome, the ultra-talented high school lefty taken with 12th overall.
In all, the Red Sox have signed 14 of their 40 picks and 11 of the top 20.
Ian Browne has covered the Red Sox for MLB.com since 2002. Follow him on Twitter @IanMBrowne and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.