"The chamber imposes on you an additional 12 months, one year, imprisonment," presiding judge Bertram Schmitt told Bemba, adding a "substantial fine" was necessary "to discourage this kind of behaviour".
Prosecutors had asked for eight years for Bemba, who is already serving 18 years after being convicted of war crimes by his marauding troops, who he sent into the Central African Republic in 2002 to 2003 to put down a coup against the then president.
Bemba was found guilty in October of masterminding a network to bribe and manipulate at least 14 key witnesses, and had "planned, authorised, and approved the illicit coaching" of the witnesses to get them to lie at his main trial.
The heavy-set Bemba, 54, wearing a dark suit and light blue shirt, showed no emotion on Wednesday as the additional sentence was imposed by Schmitt in the heavily protected courtroom in The Hague.
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The year-long sentence will run consecutively to his 18 years' jail time.
He was also ordered to pay a 30,000-euro (USD 32,000) fine.
Bemba's legal case manager Jean-Jacques Mangenda received two years; Narcisse Arido, a defence witness was given 11 months and Congolese lawmaker Fidele Babala was given six months.
All the sentences were well below what the prosecution had requested and none except for Bemba will effectively spend time behind bars, as the judge gave credit for time already spent in the ICC's detention centre.
Set up in 2002 to prosecute the world's worst crimes, the ICC goes to great lengths to try to protect witnesses and its trials from any interference.
The charges against Kenyan President Uhuru Kenyatta and his vice-president William Ruto had to be abandoned by the ICC due to a lack of proof amid allegations of witness tampering.
"The type of sentence, whether heavy or light, will send a clear message about the gravity of the crime," said Mariana Pena, from the Open Society Justice Initiative, an international law advocacy group.