Thousands turned out for Gebremedhin's funeral
Tsehaye Woldeselassie was found guilty of shooting dead Kinfe Gebremedhin in a case which shocked the country.
Death sentences are extremely rare in Ethiopia and this is only the second execution carried out since the present government came to power.
It remains unclear whether the killing had a political or personal motive.
The authorities did not say how Tsehaye was killed but executions are carried out by firing squad under Ethiopian law, Reuters news agency reports.
Gebremedhin had been a fighter for the Tigre People's Liberation Front in its 1980s war against the military government.
After the TPLF's eventual victory he emerged as Ethiopia's chief of security and immigration and as a right hand man to Prime Minister Meles Zenawi.
Then one day in May 2001 as he walked in to the armed forces officers' club in Addis Ababa, a fellow member of the TPLF, Maj Tsehaye Woldeselassie, shot him in the head at point blank range.
Thousands turned out for his funeral in the capital, Addis Ababa.
Tsehaye was quickly arrested and eventually convicted of the murder.
The BBC's Elizabeth Blunt in Addis Ababa says that at the time, speculation was rife about the motive for the killing.It was a time of tension within the TPLF with some members unhappy about the outcome of the war against Eritrea and bitter divisions inside the politburo of which Kinfe Gebremedhin was a member.