Mowbray told West Brom's website: "Craig will bring qualities to our team that we lacked last season. He still has room for development in his game. "He will hopefully progress here as a footballer. Craig has shown desire and determination to do well in England."
He added: "Craig already has Champions League and international experience. His main attributes are playing on the shoulder of the last defender. He utilises his pace and power well and manages to get in behind defences to score goals."
The fee for Beattie, who has been capped four times by Scotland and scored once, may increase by a further £500,000 depending on performance-related add-ons.