Maj Gen Muhoozi Kainerugaba has risen rapidly within the military, fueling speculation that he is being groomed to become president one day.
Analysts say his new role, working more closely with state house, will broaden his remit and experience.
Mr Museveni, 72, is one of Africa’s longest-serving leaders.
He came to power in 1986 after winning a five-year guerrilla war – and last year won his fifth term in office with more than 60% of the vote.
Gen Kainerugaba, 42, had been in charge of the Special Forces in charge of his father’s security since 2008.
He graduated from the UK’s Royal Military Academy Sandhurst in 2000 and last year was promoted from brigadier to major general.
Muhoozi Kainerugaba, 42, was promoted from brigadier to major general last year
“Muhoozi… is going to play a significant role in a post-Museveni Uganda, there’s no doubt about it,” political commentator and rights activist Nicholas Opiyo told the Reuters news agency.
“He is just giving the boy a hand in experiencing how government works on the side of politics.”
In the reshuffle Brigadier Peter Elwelu, who oversaw a deadly raid in November on the palace of a regional king accused of launching a secessionist movement, was promoted to army chief.
The BBC’s Patience Atuhaire in Kampala says the promotion is being seen as a reward for the operation, in which more than 60 people were killed.
Meanwhile the previous army chief General Katumba Wamala has been made a junior Minister for Works in the government after serving as the top army official since 2013, a departure seen as a demotion, our correspondent says.
Military spokesman Paddy Ankunda said the moves were part of normal changes within the institution.
Source: BBC Africa