The 29-year-old was offered a new deal by the Millers, but has decided to join the Latics despite them being relegated to League One and Rotherham still being in the Championship.
He has agreed a two-year deal with the option of a further year at the DW Stadium.
Latics boss Gary Caldwell told the club website: "He has great experience, having played internationally but he also knows the division inside out.
"He is a quality defender, a real leader on the pitch who has been a captain, with a superb attitude and we are delighted to have him on board."
Morgan joined Rotherham from Preston North End in 2012 and helped the club to successive promotions as they rose from League Two to the Championship.