As well as the 24 rescheduled dates, eight more performances have been added.
Taking to Instagram, the Easy on Me hitmaker said: "Words can't explain how ecstatic I am to finally be able to announce these rescheduled shows. I truly was heartbroken to have to cancel them.
"But after what feels like an eternity of figuring out logistics for the show that I really want to deliver, and knowing it can happen, I'm more excited than ever!
"Now I know for some of you it was a horrible decision on my part, and I will always be sorry for that, but I promise you it was the right one. To be with you in such an intimate space every week has been what I've most been looking forward to and I'm going to give you the absolute best of me."
It was reported recently that Adele had been motivated to "push forward" with rescheduling the residency when she returned to the stage for two sell-out gigs at Hyde Park in London at the start of this month.
A source said: "Adele loved performing in London and it gave her the drive to push forward with her Vegas residency. An announcement is coming in the next few weeks. Management have asked for a celebration to promote her return."