Smith and Ouzman Ltd gave £400,000 in backhanders to officials in Kenya and Mauritania for deals worth £2.26m to make ballot papers.
Sales and marketing director Nicholas Smith, 43, was jailed following an earlier trial at Southwark Crown Court.
His father, chairman Christopher Smith, received an 18-month suspended term.
The 72-year-old, who was convicted of two counts of corruptly agreeing to make payments, was told he would have to carry out 250 hours of unpaid work and given a three month curfew.
His son was found guilty of three counts of the same charge.
Both men were also disqualified from being company directors for six years, and have resigned from the company.
Smith and Ouzman, based in Eastbourne, which specialises in security documents such as ballot papers and certificates, was also convicted of the same three offences and will be sentenced in October.
The hearing will also deal with confiscation proceedings against the company and the individuals.
It is the first time a British company has been found guilty of bribing foreign agents, and follows an investigation by the Serious Fraud Office (SFO).
It targeted Kenya just after the 2007 political and humanitarian crisis, which was sparked by election malpractice and cost 1,300 lives and displaced 600,000 people.
Judge David Higgins said the case bore the marks of "tragedy", and the pair were guilty of a "premeditated, pre-planned, sophisticated and very serious" crime.
"In short, your behaviour was cynical, deplorable and deeply anti-social and suggests, at least in this context, moral turpitude," he said.
The company's international sales manager, Timothy Forrester, 57, was acquitted of three counts of making corrupt payments, while sales agent Abdirahman Omar, 38, was cleared of one count of corruptly agreeing to make payments in relation to a contract in Somaliland.
In a statement following the sentencing, the company said it fully accepted accountability for the actions of its directors and apologised unreservedly.
It said it had co-operated fully with the SFO throughout its investigation.
"During this period we have learned many lessons and as a result have developed industry leading, anti-bribery and corruption management processes."
Smith and Ouzman provided the certificates of authenticity for customers who bought the ceramic poppies from the Tower of London that made up the Blood Swept Lands and Seas of Red installation last year.
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