The answer is: technically no, but it's complicated.
Neither the internationally accepted definition of what constitutes a 'war crime' nor the provisions protecting the civilian population existed until the end of the WW2. The former was born with the Nuremberg Principles in August 1945; the latter came with the birth of the Fourth Geneva Convention in August 1949. From that perspective, the allied terror bombings were in fact not war crimes, as discerned by the principle of Lex prospicit, non respicit where a given action does not constitute a criminal offence if it was not prohibited by the law at the time of its commission. By that standard neither do many actions by the defeated Axis powers.
On the other hand: the Nuremberg Charter and the Tokyo Charter, used as a foundation for the post-war prosecutions, were themselves both in violation of the aforementioned principle — which did not stop them from being applied retroactively against 24 German and 28 Japanese leaders, not counting thousands of other war crime suspects tried in minor prosecutions between 1945 and 1949. The Allied powers, working together in the International Military Tribunal, argued that they're merely prosecuting the acts resulting from breaches of the natural law; a law that holds the supremacy over the existing civil law.
By this standard, assuming it held any water from the philosophical standpoint, U.S. President Franklin D. Roosevelt and British prime minister Winston Churchill would be the first names on the list of suspected war criminals responsible for mass bombings in Germany and Japan. With them, high-ranked air force commanders like General Henry H. 'Hap' Arnold, General Curtis LeMay (both USAAF), Marshal Charles Portal, Marshal Arthur Travers Harris and Air Vice Marshal Sidney Osborne Bufton (all RAF) would make the cut as the facilitators of the bombings in the Combined Chiefs of Staff and outside of it, on an operational level.
To make things even more interesting, the 1929 Geneva Convention on Prisoners of War, Part III, Article 7 states: "As soon as possible after their capture, prisoners of war shall be evacuated to depots sufficiently removed from the fighting zone for them to be out of danger. (...) Prisoners shall not be unnecessarily exposed to danger while awaiting evacuation from a fighting zone". That Convention, ratified by the United Kingdom in June 1931 and by the U.S. in February 1932, was still in full force during the WW2, creating serious, even if merely hypothetical, legal implications in itself.
During the course of WW2, POW camps existed is multiple Axis cities affected by the Allied mass bombing campaign. For example: Stalag III-D in Berlin, Oflag X-C in Lübeck, Stalag VI-D in Dortmund, Ōmori Camp in Tokyo, Chikko Camp in Osaka or Innoshima Camp in Hiroshima. Given that the Article 7 does not specify the source of the danger to the POWs and that the air raids unilaterally expanded the fighting zone beyond any protective measures available to the Axis powers, it would've been a valid legal point to assert that at least some Allied mass bombings stood in the violation of the 1929 provisions... for their own POWs.