The 24 year-old was a target for the English club in January but did not get the move he wanted then but will finally sign for the club despite his high release clause.
United have reportedly paid the 36 million euros needed to get their target and will formally be presented by the club on June 27 on an annual wage of 3 million euros.
The deal for Herrera has been completed before the 1st of July meaning that they will save 4 million euros in the transfer fee with the release clause moving up to 40 million euros if he remained with the Basque side until then.
The former Zaragoza player made 33 league appearances with 5 goals and 6 assists which helped his side to finish in the last Champions League spot.