Sordell arrives on a season-long loan deal from the Reebok Stadium having scored eight goals in all competitions for the Trotters last season. He was also selected for the Great Britain Olympic football team during the 2012 Games.
With 22 Welsh international caps to his name, free agent Church also arrives with good pedigree having agreed a two-year contract following his release from Reading.
Addicks boss Chris Powell was delighted with his new additions and confirmed the club's forward line was an area he was looking to strengthen.
"It's no secret that we were looking to bolster our striking options and I'm really happy to welcome Simon and Marvin to the club," the former England defender told Charlton's official website.
"They are two hungry, young strikers with points to prove and I look forward to working with them both."