Judge Douglas Yau handed down the sentence in Hong Kong after convicting Yeung, 54, of five counts of money laundering earlier this week.
Yeung bought into Birmingham City in 2007 and acquired the rest in 2009.
But he resigned from the parent company - Hong Kong-listed Birmingham International Holdings Ltd (BIHL) - while he awaited the verdict.
It is not yet clear what his conviction and imprisonment means for Birmingham City.
And the case raises difficult questions about how Yeung managed to pass the Premier League's fit and proper persons test whilst buying the club.
It is the first time that someone still involved in a football club would fail the owners and directors test.
Yeung was found guilty of laundering around £56m through his accounts between 2001 and 2007.
His defence lawyer told the judge that Yeung, who built a business empire that included hair salons, fertiliser and real estate, "came from rags to riches, and he's likely to return to rags".
Pleading for a light sentence, his lawyer said there had been "no subterfuge" in Yeung's business dealings as the accounts in question were held in his own name and his father's.
Throughout the trial, Yeung and the prosecution painted very different pictures of how the tycoon made his money.
The prosecution says the huge sums of money passed through five accounts from "unknown parties without any apparent reason".
Yeung insists he accumulated his millions through stock trading, hair salons, business ventures in mainland China and investing in casinos in Macau.
The jailing of Yeung leaves Birmingham fans uncertain about their club's future.
Dave Farrell, board member of Blues Trust, told Sky Sports News earlier this week: "The future of Birmingham City football club really rests in BIHL's hands now.
"Whilst we know that Carson is a major influence in that, we need to know what's happening with the football club.
"Concerns have always been there. They have been there from day one and they are still there today, but we have more support now, more galvanised fans. Support that has a concern about where we go together and how we support our club."