The 24-year-old Brazilian wing-back will spend the season in Serie A after struggling to establish himself as a regular starter since joining Dortmund from Manchester City.
As part of the agreement, Como will pay Couto's full wages for the season, reducing Dortmund's wage bill by around five million euros. The Bundesliga club are also expected to receive a loan fee of up to three million euros.
The deal reportedly includes an option for Como to make the move permanent for a fee between 20 million euros and 22 million euros.
Speaking after completing the move, Couto said he was excited to begin the next chapter of his career.
"I'm very happy to be here. I really like the team's style of play and its philosophy, and I hope I can help the team improve even more," the Brazilian said.
Dortmund paid a total of 25 million euros to sign Couto, but he was unable to secure a consistent place in the starting line-up at Signal Iduna Park.
The move gives Couto the chance to play regular first-team football and compete in the UEFA Champions League with Como.
