The off-spinner was a key member of the side that won an Ashes series in Australia for the first time in 24 years.
He is in England's Cricket World Cup squad but has not travelled to Bangladesh as his wife is due to give birth.
At Nottingham Magistrates' Court on Wednesday Swann's trial, which has faced several adjournments because of his sporting commitments, came to an end as District Judge Julia Newton said it had not been proved that a blood sample taken from Swann on the night he was pulled over could be used as evidence.
At previous hearings the court heard he was stopped by officers on patrol in the West Bridgford area of Nottingham on April 2.
The court was told he had drunk three or four glasses of white wine earlier in the evening to celebrate his birthday.
When he returned to his £350,000 detached house in West Bridgford, he found one of his and wife Sarah's two cats - called Max and Paddy - stuck under the floorboards after builders had been working on their home.
Unable to find a screwdriver to undo the floorboards, Swann decided to drive his new white Porsche Cayenne to the nearest 24-hour Asda to buy a set of screwdrivers, the court heard.
The judge said: "On the evidence I have heard, I can't be sure that the 2ml sample of blood was insufficient or incapable of analysis by ordinary means.
"It may have been possible to analyse.
"It follows therefore that, in the specific facts in this case, I am not sure that the Crown can rely on the second sample of blood and therefore I find Mr Swann not guilty."
Leaving court Swann, dressed in a black suit and black coat, did not offer much reaction to the verdict but told reporters: "I'm just looking forward to getting on with it - child due on Thursday, and winning the World Cup."
Swann's solicitor, Phillip Lucas, previously argued that there was no case to answer because one of the samples of blood taken from Swann on the night he was stopped could not be used as evidence.
Mr Lucas said that, because two samples were taken but the first could have been used for testing, the second should not be relied upon under legal guidelines.
That second sample had 83mg of alcohol in 100ml of blood, which is over the legal limit of 80mg.
Mr Lucas also argued that the blood sample taken from Swann may have been contaminated.
Defence expert Dr John Mundy, a forensic alcohol consultant who previously worked for the Metropolitan Police's laboratory, said sometimes samples could be contaminated by the rubber bungs used in the vials, which may have happened, especially if the nurse who took the sample, Lisa Hodgkinson, had "agitated" the blood by moving it up and down.
Dr Mundy said: "If you get a bung that has contaminants - and they do have contaminants, I have seen quite bad contamination - that can get into the blood and as such can interfere with the alcohol analysis one way or another."
He said the contaminants could add to the alcohol reading, making it higher than it really was.
But at a previous hearing, Ms Hodgkinson told the court that Swann told her he had been drinking for more than four hours on the night he was pulled over.
She said: "Mr Swann stated he drank approximately five glasses of white wine, which were home measures.
"He stated he started drinking at approximately eight in the evening and finished drinking about half twelve or one in the morning."
The court heard that she took a second sample of 5ml of blood from Swann as she feared her first sample of 2ml was not enough.
But Dr Mundy said the first sample would have been adequate.
He said tests could be carried out on as little as 0.24ml of blood.
The court heard that samples are split into two for tests, but Dr Mundy said technically the first 2ml sample could have been used as 1ml was "ample".
He said: "I think this sample should have been sent to the laboratory."
"As the day-to-day head of the Metropolitan Police laboratory, if this had been done in the daytime, which this wasn't, obviously, an officer would have phoned me up and said 'Will this be OK?' and I would have said 'Yes'."