TL;DR: It's complicated... Evidence shows that Hitler genuinely tried to become vegetarian in the early 30s, with some failings at times due to occasional consumption of ham, liver dumplings or some of the chefs adding meat without telling him.
Ian Kershaw - historian notable in particular for his biographies on Hitler and nazi Germany - published several references on Hitler's vegetarianism as early as 1924, per the book — Hitler, 1936-1945: Nemesis.
Chapter 7 - Mastery over the Movement
Hitler spent Christmas Eve 1924 at the Hanfstaengls’ in their splendid
new villa in Munich’s Herzogpark. He had put on weight during his time
in prison, and looked a little flabby. [...] [Hanfstaengl] noticed
that Hitler had a good appetite during the meal of turkey followed by
his favourite Viennese sweet pastries, but that he scarcely touched
the wine. Hitler subsequently explained that he had begun on leaving
Landsberg to cut out meat and alcohol in order to lose weight. He had
convinced himself that meat and alcohol were harmful for him, and,
‘in his fanatical way’, went on Hanfstaengl, ‘finally made a dogma
out of it and from then on only took vegetarian meals and alcohol-free
Chapter 8 - Breakthrough
Albert Krebs, the one-time Gauleiter of Hamburg, related a scene from
early 1932 that reminded him of a French comedy. From the corridor of
the elegant Hotel Atlantik in Hamburg he could hear Hitler
plaintively shouting: ‘My soup, [I want] my soup.’ Krebs found him
minutes later hunched over a round table in his room, slurping his
-Kershaw: Hitler A Biography, [Hitler, 1889–1936: Hubris first published 1998 Hitler, 1936–1945: Nemesis first published 2000 This one-volume abridgement with a new Preface first published by Allen Lane 2008 / Published in Penguin Books 2009].
If the historical records indicate that Hitler was vegetarian started as far back as the early 30s, rumors of his diet were already spread at the time, see for instance the New York Times article: 'At Home with the Fuhrer.' 30 May 1937, available here.
We have a pretty recent testimony (December 2012) confirming the vegetarian diet from Elizabeth Kalhammer, one of Hitler's former maids. She got interviewed several times. Here is an article from Stripes:
"He was a vegetarian. He never ate any meat during the entire time I
was there," Woelk said of the Nazi leader. "And Hitler was so paranoid
that the British would poison him - that's why he had 15 girls taste
the food before he ate it himself."
With many Germans contending with food shortages and a bland diet as
the war dragged on, sampling Hitler's food had its advantages.
"The food was delicious, only the best vegetables, asparagus, bell
peppers, everything you can imagine. And always with a side of rice or
pasta," she recalled. "But this constant fear - we knew of all those
poisoning rumors and could never enjoy the food. Every day we feared
it was going to be our last meal."
I found additional details of her job from this source, spanning from 1942 onwards:
Margot Wölk, (born 27 December 1917), is a German former secretary who
was one of 15 young women who, in 1942, were selected to taste German
leader Adolf Hitler’s food at the Wolf’s Lair in East Prussia for some
two and a half years in order to confirm that the food was safe to eat
and didn’t contain any harmful toxins or poisons.
There is also this article from France24 reporting on a study done on Hitler's death done in 2017, which based a large part of its analysis on the teeth, noting:
"The analysis of Hitler’s bad teeth and numerous dentures found white
tartar deposits and no traces of meat fibre. The dictator was
vegetarian", Charlier said.
As such, there is strong evidence that he at least tried to be a vegetarian. There are, howevever, also plenty of reports indicating that it wasn't a 100% vegetarian diet, due to the occasional liver dumpling, and sometimes other people would screw up his diet. For instance, this BBC news reports on the testimony of one of Hitler's secretary, indicating:
Such things included his modest appetite, and the way he ate only side
dishes - always avoiding meat.
His Austrian cook Kruemel believed that life without meat was not
worth living, and would often try to sneak a little animal broth or
fat into the meal.
"Mostly the Fuehrer would notice the attempt at deception, would get
very annoyed and then get tummy ache. At the end he would only let
Kruemel cook him clear soup and mashed potato."
To sum it up: it appears that Hitler was at least the majority of the time trying to follow a vegetarian diet, with some failings but not solely on his part.