The body of Eva Rausing, 48, was discovered at the couple’s house in Belgravia, London, on 9 July.
Hans Kristian Rausing, 49, was sentenced to 10 months in custody, suspended for two years, at Isleworth Crown Court.
Judge Richard McGregor-Johnson said the case illustrated the “utterly destructive effects of drug misuse”.
A second two-month prison sentence, also suspended for two years, was imposed to run concurrently after he admitted a charge of driving while unfit through drugs.
Hans Kristian Rausing was also ordered to attend a residential drug rehabilitation treatment programme for two years.
Police discovered the body of mother-of-four Eva Rausing in an advanced state of decomposition after they arrested her husband.
In a statement read to the court earlier, Hans Kristian Rausing said he had been unable to confront the reality of his wife’s death.
The court heard that Hans Kristian Rausing told police in a statement after his arrest: “I do not have a very coherent recollection of the events leading up to and since Eva’s death.
“Safe to assure you that I have never wished her or done her any harm.”
He added: “I did not supply her with drugs. I have been very traumatised since her death.
“I do not know what caused her death. I did not feel able to confront the reality of her death.
“I do not feel, with the benefit of hindsight, that following her death I acted rationally.
“I tried to carry on as if her death had not happened and batted away any inquiries about her.”
In a separate statement read to the court, Hans Kristian Rausing’s doctor said his patient had told him: “I know it sounds selfish but I just didn’t want her to leave.”
His doctor described him as a shy, socially awkward man who could not cope with the overwhelming emotional trauma of his wife’s death.
Hans Kristian Rausing was stopped by police on 9 July on suspicion of driving under the influence of alcohol or drugs.
A subsequent search of the couple’s home led to the discovery of Eva Rausing’s body under a pile of bin bags, clothing and bed linen in a room which had been sealed with gaffer tape.
A post-mortem examination to determine the cause of her death proved inconclusive.
Medical reports showed that she probably died on 7 May. Initial toxicology reports showed the presence of drugs in her system.
Prosecutor James O’Connell said Eva Rausing had expressed concerns about her husband’s “chaotic lifestyle” to her financial adviser on 3 May, the last time she was seen by witnesses.
Hans Kristian Rausing’s family is said to be worth more than $6 billion.
They made their fortune from the Tetra Pak carton firm, although the family exited the company in 1995.
In sentencing, Judge McGregor-Johnson told Hans Kristian Rausing: “You and your wife had every material advantage imaginable, and for a time a happy family life.
“Your relapse into the misuse of drugs, together with that of your wife, destroyed all that.
“It is graphically illustrated by the contrast between the rooms visitors saw and the utter squalor of the rooms you really lived in.”
The couple had struggled with drug addiction for many years.
After an earlier court appearance, Hans Kristian Rausing’s parents issued a statement, saying they hoped their son could “find the strength to begin the long and hard journey of detoxification and rehabilitation”.
In 2008, Eva Rausing and her husband faced drug charges after crack, heroin and 52 g of cocaine were found in their home.
Eva Rausing had been arrested after she allegedly tried to smuggle small amounts of crack cocaine and heroin into the US embassy in London.
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