Annan's declaration on Thursday starts the clock ticking on the three-month period the investigators have been given to complete their work, although the UN Security Council can extend the deadline if needed.
The inquiry was ordered by the Security Council after UN experts concluded Lebanon could not conduct a credible investigation on its own.
German prosecutor Detlev Mehlis, the team leader, arrived in Beirut three weeks ago with four aides to carry out the groundwork.
"But we have strengthened the team as days have gone by and, as of today, it is fully operational," Annan said.
Al-Hariri's death came in a 14 February bomb attack in central Beirut that killed at least 20 other people.
Some Lebanese blame Damascus for the killing, but Syria has denied involvement, as it has in a second Beirut bombing on 2 June that killed anti-Syria journalist Samir Kassir.
Damascus exerted virtually unchallenged control over Lebanon for three decades but said at the end of April that it had withdrawn all its forces from its neighbour in line with Security Council Resolution 1559, adopted in September.
A UN verification team subsequently confirmed that Syria had withdrawn all its soldiers but could not say for sure whether it had pulled out all its intelligence agents.
Annan said he sent back the team after being told "there were other elements that may have gone back to Lebanon".