"thus finally" is correct and can be used in written English.
You can use it to indicate that a particular situation or action has been reached after a period of time or effort. For example, "Thus finally, John had saved enough money to buy his own house."
The Carolingian empire thus finally disintegrated.
Seierstad describes it thus: Finally, he was standing there in a room of uniformed men in his underpants.
Dikshit was recently fined a similar amount after pleading guilty to an online betting charge in the US, thus finally settling his dispute with the Department of Justice.
Mashtags Birds Eye product that shapes potato into @ and # symbols, thus finally giving children the opportunity to pretend they're posting on Facebook while eating their dinner.
Thus, finally the potential of porting a CAA method to the graphics processing unit (GPU) is shown in one example.
Arendt's unqualified support of Heidegger was important in establishing the convenient myth that his Nazi involvement had been, as she put it, a case of an unworldly man getting carried away by politics, and thus "finally a matter of indifference".
The reader's sense of where his heart lies became very clear when Caroline tells him of her plans to vacate Hundreds Hall, and thus finally to disappoint his hopes of possession.
It will, at last, fully embrace the Internet protocol (IP), the Net's lingua franca, thus finally catching up to the standard for computer networks.
Although the country was now quite calm, Pelloux attempted to make his earlier bill more repressive, thus finally uniting the left in opposition against him.
Simple changes to the legislation would allow them to benefit from both programs, and thus finally receive the compensation they deserve.
On Nov. 16, 1700, however, Austria and Prussia signed a secret treaty that permitted Frederick to crown himself king in Prussia, thus finally realizing his long-cherished ambition.
