Swedish defender Eriksson spent six successful years with Women's Super League champions (WSL) Chelsea, winning five league titles, four FA Cups, two League Cups, and the Women's Community Shield.
Harder, 30, joined Chelsea from VfL Wolfsburg in 2020 for a fee in excess of £250,000 ($315,525) -- then a world record transfer fee for a female footballer.
"Pernille and Magdalena are two top players with a lot of experience," Bayern head coach Alexander Straus said in a statement.
"They've won several trophies, participated in many big tournaments, at club level and also on the international stage with their national teams.
"They're a perfect addition to our team and bring even more quality to our talented squad. They'll take us to the next level. We're very excited about this."
Both players, who are a couple, had said they would be leaving Chelsea last month upon the expiry of their contracts and were linked to several prominent European teams.