New York state Sen. Malcolm Smith tried to buy entry onto the New York City mayoral ballot by orchestrating bribes to Republican leaders, federal prosecutors charged Tuesday as they revealed details of a wide-ranging corruption probe that also ensnared a Queens council member and four others.

The criminal complaint unsealed Tuesday alleges a web of illegal activity connecting bribes on behalf of Mr. Smith's political ambitions to an upstate real-estate transaction and the use of state and New York City Council discretionary...