Poythress, a 6-8 forward out of Clarksville, Tennessee, is ranked 15th in the class by Scout.com.
Goodwin, a 6-5 guard from Little Rock, Arkansas, is ranked by Scout.com at 17th in the class.
The McDonald's All-American game also features Kentucky three top targets in the class of 2012. The three are 6-10 center Nerlens Noel, Scout's top ranked player since reclassifying from 2013; 6-5 swingman Shabazz Muhammad, rated 2nd in the class by Scout; and 7th ranked 6-7 forward Anthony Bennett.
Poythress will play for the East squad, and Goodwin will suit up for the West team. The game will be played in Chicago at the United Center on March 28. Game time is scheduled for 9:30 p.m. ET, and the game will be televised on ESPN.
Poythress and Goodwin had previously been named participants in the Jordan Brand Classic.