As part of the shake-up, the cabinet appointed Brigadier-General Elias Koeikati as acting head of the State Security Department, which falls under the Interior Ministry.
Information Minister Ghazi Aridi said the government had also decided to disband the unit eventually as part of plans to consolidate the security services.
The appointment came two days after the cabinet moved to purge Lebanon's security services of Syrian influence by naming new security and police chiefs.
On Tuesday, the government appointed a replacement for a general detained as a suspect in the assassination of former prime minister Rafiq al-Hariri and removed a police commander associated with the former pro-Syrian administration.
The information minister said the cabinet did not discuss a plan to overhaul the security services, on which it had deferred a decision on Tuesday.
Lebanon's police force is short of
11,000 personnel and equipment
The bombs, which have killed six people since February, have generated widespread fear in Lebanon, particularly as the government has acknowledged it is nowhere near arresting the culprits.
Aridi said: "The cabinet has decided to ask the interior minister to announce a financial reward to anyone who provides information on terrorist attacks that are carried out in Lebanon, and to anyone who helps track down and apprehend the culprits."
The government has accused unknown "terrorists" of planting the bombs, the latest of which severed the left arm and leg of a well-known woman journalist who hosts a TV talk show.
Prime Minister Fuad Siniora promised on Wednesday that the Lebanese government would eventually catch the people responsible for the bombings that have occurred since a massive explosion killed al-Hariri and 20 other people on 14 February.
PM Fuad Siniora has vowed
to bring bombers to justice
Siniora announced the formation of an operations centre to coordinate activities and share intelligence among the various security services.
But he told parliament that, despite new recruitment, the 18,000-member police force is still short of about 11,000 personnel and lacked equipment.
Siniora, who is backed by the anti-Syrian majority in parliament, did not blame anyone for the explosions. But anti-Syrian groups have accused Syria and its remaining allies in the Lebanese security services of being behind the al-Hariri assassination and subsequent bombings.
Syria has denied the allegations.