Lothian's fleet of 42 Falkirk-built vehicles will also see travellers alighting through middle doors for the first time in a decade to speed up services.
The 45ft long buses will be able to accommodate a total of 131 passengers, including those standing.
Other features on the six-wheelers include high-back seats to give passengers more personal space.
Lothian managing director Richard Hall said they would be introduced in late January, on routes still to be decided.
He said: "We are trying to create an atmosphere that feels comfortable, safe, warm and welcoming.
"We want bus travel to be somewhere nice to be that delights the passenger.
"It's the best spec bus in the UK."
Mr Hall said enticing people out of their cars required "something that really gives them a first-class experience".
Lothian scrapped middle doors in 2009 but will be the first in Scotland to reinstate them, in an attempt to reduce delays at bus stops.
Mr Hall said: "We wanted to look at how to speed up alighting and journey times, and improve passenger flow.
"It can take up to three minutes to empty a double decker, and people can't get on and off at the same time."
However, he said few people would try to board through the middle door to dodge fares.
He said: "There is more CCTV and we have inspectors, so the revenue risk is absolutely minimal."
People in wheelchairs will continue to board and alight at the front door.
Alexander Dennis chief executive Colin Robertson said the unveiling of the bus at its factory in Camelon yesterday was a "momentous day" for the company.
The buses are the first to be built by Alexander Dennis for Lothian for seven years and the first fleet for around 20 years.
The Enviro400XLB vehicles comprise a Alexander Dennis bodywork on top of a Volvo engines and chassis.
Transport secretary and Falkirk West MSP Michael Mathewson said: "There was always that missing piece of the jigsaw in not having Alexander Dennis buses on the streets of Scotland's capital city."
Gavin Booth, director passenger watchdog Bus Users Scotland, said: "Lothian’s new mega double-decker combines comfort and capacity for bus passengers, and the extra seating will be welcomed when they take to the Edinburgh streets.
"It is good to see the bodywork on these impressive new buses was built in Falkirk."
However, Edinburgh City Council opposition Conservative transport spokesman Nick Cook tweeted: "Huge missed opportunity from Lothian Buses - with these new buses offering only one space for wheelchair OR buggy.
"How can such moves give any confidence that the city council's drive to ban cars won't reduce city centre accessibility for disabled and parents."