Series two of Kay Mellor's acclaimed show will focus on five low-paid hospital workers in Bradford who win £72 million in the EuroMillions lottery draw.
Addy will play recovering alcoholic Alan, who finds himself tempted by the booze following the big win, while Finneran is cast as nurse Mandy.
Natalie Gavin (Prisoners' Wives) will star as Mandy's daughter Becky, a single mother whose numbers win the jackpot, while Jimi Mistry (Strike Back) is male nurse Tom, who decides to have a baby with his girlfriend following the win.
Gavin & Stacey's Alison Steadman is the final member of the syndicate, former dancer Rose, who hopes to pick up where she left off with the help of an expensive double knee replacement.
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"The Syndicate is a drama series of our time," said writer Mellor. "As the world recession bites harder and deeper, more and more people are doing the lottery. It gives them the weekly hope of winning their way out of debt and poverty. They are five little balls away from living their dream or so they think!"
BBC One's Polly Hill added: "We are delighted to be making a second series of the acclaimed drama The Syndicate. Kay's brilliant scripts have once again attracted an incredible cast that will make this drama a real treat for the BBC One audience next year."
The first series of The Syndicate starred Timothy Spall, Lorraine Bruce, Matthew Lewis, Matthew McNulty and Joanna Page as supermarket workers who won a big cash prize.
The Syndicate will return to BBC One for a second series in 2013.
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Watch a trailer for the first series of The Syndicate below: