Awil Dihar Salad, two security staff and his driver died in the first blast, a suicide car bomb at a checkpoint near the presidential palace.
The deputy-governor of the local region was among those who were injured.
There were further casualties in the second blast. Militant group al-Shabab said it carried out both attacks.
At least 17 people were injured in the explosions, Reuters reported.
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Mr Salad, 45, was a veteran reporter who worked to revive the country's media before leaving the country in 2005 and returning several years later to work with Universal TV.
He had been based in Mogadishu for several years and believed the situation there was improving after years of conflict, BBC Somali reported.
Al-Shabab, which is linked to al-Qaeda, was forced out of Mogadishu in 2011 but continues to mount regular attacks in the city.
However the US has sharply increased its air strikes against the group since President Trump took power. Earlier this month the US military said it had killed 62 fighters in six air strikes.
The US State Department says the group retains control over large parts of the country and has the ability to carry out high-profile attacks using suicide bombers, explosive devices, mortars and small arms.