The 28-year-old former Sampdoria keeper worked with United boss Louis van Gaal at AZ Alkmaar and will provide competition for Spanish stopper David de Gea, should the latter remain at Old Trafford.
Victor Valdes is set to be sold after refusing to play in the reserves last season while Sam Johnstone represents another option between the sticks.
Romero told United's official website: "I am absolutely delighted to join Manchester United. To play for the biggest club in the world is a dream come true for me. Louis van Gaal is a fantastic manager and I cannot wait to get started on this new and exciting challenge in my career."