The property group, which is backed by UK-based M&G Investments, has started work on the project that will have almost 500 keys in total.
The group, headed by Patrick Crean, is commencing work on the project on Upper Abbey Street and Great Strand Street after an appeal to An Bord Pleanala about the development was withdrawn.
Marlet bought the site, which was previously owned by the hotel and pub owners Liam and Des O'Dwyer, early last year for more than €22 million.
The 239-key hotel will have an entrance on Abbey Street, while the 256-key aparthotel will front onto Great Strand Street. The development is expected to be completed in the second half of 2021.
According to the Sunday Times, Marlet is in advanced talks with a number of operators about managing the properties. Staycity is reported to be one of the parties interested in the aparthotel.
Marlet is also a major developer of Dublin office and residential schemes.