Yes, whale meat is halal (permissible) to consume.
It is clearly mentioned in the Holy Quran:
“He (Allah) has only forbidden to you dead animals, blood, the flesh of swine, and that which has been dedicated to other than Allah.”(The Quran 2:173).
“O mankind, eat from whatever is on earth [that is] lawful and good.”-(The Quran 2:168).
As far as my knowledge goes, there is no verse from the Quran or any authentic Hadith that forbids the consumption of whale meat. So it is fully halal (permissible) to consume whale meat.