Magath, a disciplinarian whose nickname Quaelix is a cross between his surname and the German word for torture, said he had ironed out his problems with the temperamental Diego, who stormed out on the team on the final day of the 2010-11 season.
He lavished praised on the 27-year-old and said he would be the team's playmaker for the upcoming season.
"It's well known that the relationship after the Hoffenheim match was tense, but we have talked it over and cleared away all the problems," Magath told a news conference.
"In our club, it's give and take, mistakes are excused. We must now look forward. Diego is Champions League material and a player of his class increases our chances of finishing high in the table.
"Diego will get the number 10 shirt. He is a central player who can create chances for team-mates and score goals himself.
"As playmaker it will be his job to get the most out of his team-mates.
"I ask our followers to give him a second chance. Anyone who loves football will love a player such as Diego."
"It's important that we learn from our mistakes, to do things better next time," added former Santos, Porto, Juventus and Werder Bremen midfielder Diego, sitting alongside his coach.
"That is what I would like to do now. I hope then fans can forgive me."
Diego, who has not featured for Brazil's senior side since the 2007 Copa America, left the team hotel in a fit of pique after being told he would not play in a match against Hoffenheim. He did not go to the stadium to watch the match.
Last year, he helped Atletico win the Europa League.