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.”
Romero has featured 62 times for Argentina and played in the 2014 World Cup final, which the Albiceleste ultimately lost to Germany in Rio de Janeiro.
He made his senior club debut at Racing Club de Avellaneda in 2007 before moving to AZ and then on to Sampdoria. His performances for the Genoa-based outfit helped them secure promotion to Serie A in 2012 and he was sent to Monaco on loan for the 2013-14 campaign.
Dutch manager Van Gaal, under whom Romero celebrated an Eredivisie title win at AZ in 2009, said: “Sergio is a very talented goalkeeper.
“He was a young keeper during my time at AZ Alkmaar and I am delighted he is joining Manchester United.
“He had a fantastic World Cup last summer in Brazil, although that is something I have put to the back of my mind!
“He will be a great addition to the team and I am looking forward to working with him once again.”
While Romero was now eligible to link up with his new team-mates in the United States ahead of a friendly meeting with Paris St Germain in Chicago, winger Angel Di Maria failed to board his flight to California.
The former Real Madrid player was due to meet up with United’s tour party in San Jose on Saturday.
Di Maria’s absence has fuelled speculation a move to PSG is moving closer but United have refused to comment on reports in France that they have agreed to sell him to the Parisian club for 65million euros (#46million).