Jiang, whose term as head of the powerful military commission was to have run until 2007, handed in his resignation on Sunday during a meeting of the ruling Communist party's Central Committee.
The committee approved Hu's takeover of the Central Military Commission chairmanship after accepting Jiang's resignation, the official Xinhua news agency reported.
Former vice-director in the People's Liberation Army, Xu Caihou, 61, will replace Hu as deputy chairman.
Hu had long been expected to become chairman, after he assumed the presidency from Jiang and became general secretary of the Central Committee in March last year.
But Sunday's decision was a surprise to diplomats and political analysts, who did not expect any major announcements from the Central Committee's closed-door meeting.
Taking the top military post will ensure Hu's status as the country's paramount leader, although he is still surrounded by Jiang allies on the nine-member Standing Committee, the party's highest echelon of power.
Jiang's resignation is seen as likely to better institutionalise leadership transitions and give Hu more scope to promote his political agenda, reforming the party and modernising its functions.
Jiang was meant to head the
military commission until 2007
The former president had held the top military position since November 1989 and did not relinquish the post - arguably the most powerful in the country - when he made way for Hu as president last year.
Sources had said prior to the announcement that there was much pressure within the Central Committee for Jiang to retire, following in the footsteps of late paramount leader Deng Xiaoping, who resigned as chairman of the military commission in 1989 in favour of Jiang.
They also indicated he could still wield influence even after stepping down, citing the example of Deng, who gave up all his official posts in 1989, but continued to hold power with no title for years.
Jiang's leadership oversaw phenomenal economic growth, gradually leading China towards the centre of global affairs, presiding over ascension to the World Trade Organisation as well as Beijing's successful bid for the 2008 Olympics.
Strikingly, China experts say Jiang is still the most unpopular leader communist China has ever had, far removed from the deity-like status of previous patriarchs Mao Zedong and Deng Xiaoping.
The former president appears keenly aware of how history might remember him, and battled hard to get his personal contribution to Marxist theory, named Three Represents, placed in the Communist party charter.
The four-day session of the Communist party's 198-member Central Committee began behind closed doors on Thursday and was to focus on ways to improve party governance.