The ruling Conservatives see allowing gambling as vital for the tourism industry, creating jobs and attracting big spenders, particularly after last year's international financial bailout.
Cyprus's previous communist government, in power until early 2013, had flatly refused to entertain the idea despite reported interest from foreign operators. Some Cypriots still see gambling as socially and morally undesirable.
The island draws about 2 million tourists a year, with the sector representing about 10 percent of overall output.
Authorities said they would invite expressions of interest in a two-stage selection process once approval of relevant legislation is approved by parliament.
"This will be one of the most important infrastructure projects in Cyprus in coming years," Cypriot government spokesman Nicos Christodoulides said.
The licence would be valid for 30 years, and the successful bidder would get an exclusivity agreement for 15 years. The state would charge a 15 percent tax on gross income from gambling, Christodoulides said in a statement.
(Reporting by Michele Kambas; Editing by Louise Ireland)