The visit comes amid a recent thaw in relations between Shiite Iran and the Sunni-ruled Gulf states despite high sectarian tensions over the conflicts in Syria and Iraq.
Sheikh Sabah, on his first visit to Tehran as head of state, will lead a high level delegation consisting of the ministers of foreign affairs, oil, finance and commerce and industry, the cabinet said in a statement.
It said it hoped the visit "would boost cooperation in various fields," as well as strengthening "security, stability and peace in the region," in the statement issued after the weekly cabinet meeting.
Iran's newly-appointed ambassador to Kuwait Ali Riza told reporters today the emir's visit "will give a push to regional cooperation and consolidate ties".
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He said Sheikh Sabah's talks with Iranian President Hassan Rouhani will touch on the Syrian conflict and the situation in the Gulf.
Kuwait currently holds the rotating presidency of the Gulf Cooperation Council, which also includes Bahrain, Oman, Qatar, Saudi Arabia and United Arab Emirates.
The Iranian envoy said he expected the a number of cooperation agreements in fields including aviation, tourism, sports to be signed.
In December last year, Iranian Foreign Minister Mohammad Javad Zarif started a tour of Kuwait, the United Arab Emirates, Oman and Qatar. But it ended without Zarif travelling to Iran's main rival, Saudi Arabia.
Two weeks ago, Riyadh's Foreign Minister Prince Saud al-Faisal said he had invited his Iranian counterpart to visit.
Tehran welcomed the plan and stressed the need to boost relations after years of strained ties.