Apia Regional Office Fund, which is asset-managed by Warner Estate, is modernising Yorkshire House, which stands on the corner of Greek Street and East Parade.
Office suites are available from 1,500 sq ft to 18,000 sq ft with rents from £21 per sq ft.
The main tenant is currently law firm Lupton Fawcett.
Mark Nicholson, of joint marketing agents Dove Haigh Phillips, said the building was close to a large number of restaurants and Leeds railway sta-tion.
It is also in easy walking distance of the city’s retail centre, he added.