The hotel chain said the investment programme would bring 150 jobs and 10 apprenticeships.
Two of the new hotels, located off the Royal Mile on New Market Street, will open at the end of this month.
The third, which will be in York Place in the New Town, is scheduled to open in late spring.
The new sites will take the total number of Premier Inn hotels in the city to 14, with more than 1,500 rooms.
One of the two hotels on the Royal Mile will be a hi-tech "hub by Premier Inn", the chain's first in Scotland. The hub will allow guests to control their room settings using an Apple Watch.
Additional investment by Premier Inn in the city includes a £1.8m extension at Premier Inn Newcraighall and a £1.2m refurbishment at Edinburgh Central.
Simon Ewins, chief operating officer for Premier Inn and hub, said: "We are absolutely delighted to be opening three new fantastic hotels in Edinburgh and it is great that we are able to bring so many jobs and apprenticeships to the city.
"Hub is a new concept for us which we are really excited about, especially as this is the first one in Scotland and outside of London.
"We are confident our guests visiting the beautiful city of Edinburgh will enjoy this new digital experience and we will look to open more in Scotland in the future."
Premier Inn has announced it is investing £35m in opening three new hotels and revamping two others in Edinburgh.