The 29-year-old centre-half rejected a new deal with the Championship Millers and also turned down interest from Bolton in favour of a move to the League One side.
He will officially join Latics on July 1, subject to a medical next week.
Boss Gary Caldwell told the club's official website: "We knew Craig's contract was up and he may be available, and this was somebody we were very interested in bringing to the club. We are delighted he has chosen to join Wigan Athletic.
"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 was an instrumental figure in Rotherham's rise from League Two to Championship safety as he captained the side to back-to-back promotions.
He intimated he was keen to sign a new deal at the New York Stadium, but subsequently changed his mind.
