Is it okay if I write in letter/e-mail, the following? "I have been awarded recently ..." when the final selected list for the award is published online, but the actual award offer letter is yet to receive?
In general I would say that this is perfectly acceptable (although the phrasing more accurately should not use the past, but the future tense - "I will receive the 2019 XYZ award, see ").
The only reason I see to be cautious about this is if it's not 100% sure yet that you will actually get this award. I would say if the respective agency or selection committee has already made available a public list I would count this as sufficiently certain, but if you for instance had learned about it through more informal means (e.g., your department head has received a phone call that one of his employees will receive additional funding, or something along these lines) I would be a bit hesitant to already officially brag about your award.