The Walking Dead actor will play taxi driver Vince McKee - an ordinary man who makes a terrible decision - in the three-part serial.
The Driver - from Accused writer Danny Brocklehurst - will follow Vince as he takes a job driving for a criminal gang and later seeks redemption for his sins.
Former Coronation Street actress Sacha Parkinson will play Vince's daughter Katie, with Claudie Blakeley (What Remains) cast as his wife Ros.
Ian Hart, Colm Meaney, Shaun Dingwall and Lee Ross will also star in The Driver, which will film in and around Manchester from this week and will air on BBC One later in 2014.
"I am very excited to be staring in The Driver and to be working with such a great cast," said Morrissey.
Brocklehurst added: "The Driver is a passion project for me and I'm proud of the way it is both a character drama and a thriller. As with all my work there is a strong emotional core and it explores ordinary lives pushed into extraordinary situations.
"I'm thrilled to be making such a powerful drama for BBC One. The majority of my work has been here and as writer you are given incredible authorship, which is a fantastic thing.
"I have always wanted to work with Dave Morrissey, one of the UK's finest actors, and I'm delighted to be finally getting the chance. The entire cast is amazing and it is a privilege to have them on board."
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