You can check the last year AMCAS verification thread to have an idea of how long it would take. At this point I think it should be about 1-2 weeks.
As of TMDSAS, the longest wait is for them to mark your transcript as "received." It took them 2 weeks to "receive" mine, even though I sent it from Texas. But once they have your transcript, the verification process can be pretty quick. I submitted my app June 1st, transcript received June 12th, and it was verified June 13th already.
AMCAS, on the other hand, "receives" your transcript pretty fast, but takes a while to verify. Again, just check the verification thread to estimate how long it would take.