Herrera becomes the first player to arrive at Old Trafford since Louis van Gaal, currently managing the Netherlands at the FIFA World Cup, was announced as the club's new manager last month.
The 24-year-old joins United after paying the buy-out clause in his contract at Athletic Bilbao and will boost a midfield that appeared to lack quality last season as United finished a lowly seventh in the Premier League following a disastrous campaign under David Moyes.
Former Spain Under-21 international Herrera was reportedly set to join United before the start of last season, but the transfer fell through on the final day of the British summer transfer window.
However, United have now finally secured his services.
In a statement on the club's official website, Herrera said: "Signing for Manchester United is a dream come true. I have played at Old Trafford for Athletic Club in the UEFA Europa League and it was one of the highlights of my career so far.
"I have joined United to do all I can to help the team reach the club's objectives.
"Having arrived on Tuesday, I’m excited to now be living in Manchester and I can't wait for my first game in United's famous red shirt.
"I will never forget my time with Athletic Club and I'd like to thank the fans and staff for all their support and, above all, wish all my fantastic former team-mates all the best for the future."
Herrera joined Bilbao from Real Zaragoza in 2011, and was part of the team that reached the final of the Copa del Rey and UEFA Europa League in 2011-12, beating United on the way to the showpiece of the latter competition.
In his three years at San Mames, Herrera made 128 appearances and scored 11 goals.
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