The Spanish champions posted a statement on their website in which they announced the former Madrid and Germany midfielder will be unveiled at a press conference at 12.15pm BST.
Schuster succeeds Capello, who was sacked despite leading the capital club to their first Primera Liga title in four years.
Former Germany and Madrid midfielder Schuster moves from Getafe, with whom he has enjoyed two years in charge.
Madrid president Ramon Calderon admitted yesterday the 47-year-old seemed the perfect fit for the Bernabeu vacancy.
He told El Pais newspaper: "It seems to me that his teams play good, entertaining football.
"He knows the club and knows how to handle a dressing room full of stars."
Schuster was tied to Getafe for a further season but appears to have freed himself from his current contract after Madrid insisted they would not pay a transfer fee to sign a coach.
"Schuster has told us that he has solved his situation with Getafe," Calderon said last week.
"He has always been among the three or four coaches with whom we have spoken.
"It appears logical that he will be the next coach."
Madrid sacked Italian Capello due to concerns over the team's style of play.