The operator also admitted the faster-accelerating trains would not cut Edinburgh-London journeys to four hours until 2021, as Scotland on Sunday revealed in March.
They are five months late in entering service due problems including their compatibility with signalling equipment.
The first trip was on the London King's Cross to Leeds route, with Hull to be added tomorrow.
The trains will later run on the main part of the east coast main line - as the two initial destinations are on branches.
They can operate on both electric and diesel power, enabling them to eventually run as far as Aberdeen and Inverness as the lines north of Edinburgh are not electrified.
UK Government-run LNER said Azumas would run to Edinburgh "by the end of the year".
It had told The Scotsman in March this would happen in "late summer", although industry sources said November or December was more likely.
The operator added: "With a new timetable from December 2021, more regular journeys between London and Edinburgh will take just four hours."
That will cut 20-40 minutes from trips, with the only current four-hour journey being the 5:40am "Flying Scotsman" service from Edinburgh to London.
BACKGROUND: Four-hour Edinburgh-London train journeys delayed until 2021Hitachi-built Azuma means "east" in Japanese, and the new fleet is modelled on the country's bullet trains.
Each has up to 100 extra seats compared with existing rolling stock.
The 65 trains will replace LNER's current fleet of 45 electric and diesel trains, the latter dating back to the 1970s and similar to those beign refurbished by ScotRail for its inter-city routes.
Other passenger benefits include 7cm of additional leg room in standard class, free wi-fi and electronic reservation displays.
LNER managing director David Horne said: "The new trains are really the start of the transformation on the east coast route.
"They're replacing trains which are 30 and 40 years old."
The Azumas are the same type of trains - Class 800 Intercity Express - which were launched by Great Western Railway in 2017.
Hitachi Rail managing director Karen Boswell said: "Putting trains into service is really complex.
"The balance of building new technology and working with the infrastructure is always very challenging.
LNER said passengers with bikes would have to turn up ten minutes before departure for staff to open the cycle storage area.
Nine and ten-coach Azuma trains will have eight bicycle spaces, with five-coach Azuma trains equipped to carry four bicycles, with reservations required.