I recently applied to a graduate engineering program at a university and was contacted by a professor who was interested in my application. We discussed the projects that he is undertaking and seems to think I would be a good addition to the team. A week after the interview, he reached out stating that he has instructed the university to offer me the MASc position in the program I was applying for, and discussed the courses he would be interested in having me taking and the total funding he is willing to provide for the program. I replied back stating that I would love to join his team.
My concern so far is that I have not received an official letter of admission from the university and I am not sure if it is practical or ethical to apply to other universities in the meantime in order to ensure that if things won't work out I have a backup plan.
My question: is this the right thing to do or should I wait for the decision to arrive from the main university I applied to?