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.
Atletico Madrid have reportedly moved into pole position to sign Tottenham Hotspur captain Cristian Romero as the Spanish club push to complete a deal before the European summer transfer window closes.
Vincent Kompany has made it clear that Bayern Munich's success last season will count for little unless his players show the same determination and ambition when the new campaign begins.
Real Madrid have confirmed the signing of highly-rated winger Yan Diomande from RB Leipzig after completing one of the biggest transfers of the European summer.
Vincent Kompany has made Bayern Munich's ambitions clear ahead of the new season, saying the club's main objective is to win the UEFA Champions League after strengthening the squad during the current transfer window.
