Leasing of apartments will begin Tuesday at downtown Boston’s newest luxury tower, the 26-story Radian at 120 Kingston St., in anticipation of a May grand opening.

Monthly rents start at $3,000 for studios and range up to $4,000 for two-bedroom units. Sizes range from 563 to 1,082 square feet. Prices for the tower’s penthouse units – which range from 662 to 1,471 square feet – have not been announced.

Built on the site of the former Dainty Dot Hosiery Co., the high-rise was designed by Elkus Manfredi Architects of Boston and executive architect Perkins Eastman of New York. It was developed by Forest City Boston, a subsidiary of Cleveland-based Forest City Enterprises, and Boston-based Hudson Group North America.

Common amenities on the fifth floor include furniture retailer Montage, a residents’ lounge and health club. A 4,500-square-foot ground floor space has been reserved for a restaurant with an outdoor patio next to the Rose Fitzgerald Kennedy Greenway.

"Radian serves as the gateway to the Greenway and is unique for its location within the vibrant neighborhoods of the Leather District, Downtown Crossing and Financial District that are drawing more and more residents, new businesses, boutique local retailers and cool new restaurants," Doug Arsham, vice president for Forest City Boston, said in a statement.

The leasing office is at 108 Lincoln St.