While it may not be within the 90 days HTC originally promised, executive director of product management Mo Versi announced on Twitter this morning that the Verizon edition of the HTC One has had its 4.4 OTA update approved by Verizon, and that it will begin rolling out shortly.
HTC One Verizon Owners! We have received technical approval for the OS 4.4 + Sense 5.5 update today. Expect the OTA out shortly. Thanks!
— Mo (@moversi) February 6, 2014
The 4.4 update also brings Sense 5.5 improvements to the phone, and Pocket-lint actually has a pretty great rundown of what's new in terms of features. The short version, however, is that there are some pretty substantial changes to BlinkFeed (including an "off" switch), the gallery, and some of the camera features like Video Highlights and Zoes (the latter of which now supports GIF exporting).
Verizon has yet to actually announce the update, so until then it's hard to put a firm date on when the rollout will begin, but you can probably safely assume it's going to be some time in the next few weeks.