Some of the money was likely to be spent on weapons from France, Suleiman indicated in a televised address.
One of the few institutions not overtaken by the sectarian divisions that plague the country, Lebanons army is ill-equipped to deal with internal militant groups, particularly the Shiite Muslim guerrilla and political movement Hezbollah.
The Sunni Muslim kingdom of Saudi Arabia may be seeking to bolster the army as a counterbalance to Hezbollah, seen as the most effective and powerful armed group in Lebanon and funded by the regional Shiite power Iran.
"The king of the brotherly Kingdom of Saudi Arabia is offering this generous and appreciated aid of $3 billion to the Lebanese army to strengthen its capabilities," Suleiman said.
"His Highness suggested that weapons would be purchased from France, and quickly."
French President Francois Hollande is currently meeting with Saudi King Abdullah in Riyadh.
Lebanon's armed forces have been struggling to deal with violence spreading over the border from Syrias civil war.
The country, which is still rebuilding after its own 15-year civil war, has seen clashes between gunmen loyal to opposing sides of the Syrian conflict, as well as militant attacks on the army itself.
Rising regional Sunni-Shiite tensions have been stoked by the fight in neighbouring Syria, which generally pits the countrys majority Sunni Muslim rebels against President Bashar al-Assads minority Alawite sect, an offshoot of Shi'ite Islam.