The proposal for the plot outside the city's station replaces an earlier scheme by DLA Design drawn up for site's previous owner, developer AWG.
Stephen Surphlis of McAleer and Rushe said: 'We are confident that the new City Square House will be a tremendous success story and become a flagship development for the City of Leeds.
'The plans for the new City Square House - are bold and exciting and in keeping with this very sensitive and historic area of the city.
He added: 'We believe that this development will be a very positive and welcome addition to the city centre.'
Construction is hoped to begin on site in October this year and take 18 months to complete.