The dispatch will make South Korea the biggest contributor to coalition forces in Iraq, behind the United States and Britain.
US President George W Bush praised the mission in a personal phone call to South Korean President Roh Moo-hyun.
The new contingent, a mixture of support troops and combat-ready forces, is expected to carry out reconstruction and maintain security in the region around Kirkuk, Lt Gen Kim Jang-soo said at a news conference in Seoul.
Kim, chief operation director at the Joint Chiefs of Staff, returned to South Korea on Monday after discussions in Washington to nail down details of the deployment.
A cabinet meeting on Tuesday approved a bill requesting the planned deployment. But the mission must still win the consent of parliament.
"We agreed to send the troops near the end of April," he said. "We noted that the timing could change depending on National Assembly approval."
On Tuesday, some 300 activists, mostly students, briefly scuffled with police as they tried to march towards the National Assembly to protest the troop dispatch plan.
"No more blood for Bush!" read banners held by the protesters.
Opposition to the dispatch has risen since two South Korean engineers were killed by Iraqi resistance fighters north of Baghdad late last month amid a rash of attacks on coalition personnel.
South Korea already has 460 military medics and engineers operating in the southern Iraqi city of Nasiriya.
Kim said sending and keeping the troops until the end of 2004 would cost about 230 billion won ($191 million).
On Monday President Bush thanked Roh for agreeing to send troops, Roh's office said.