is an adverb that is frequently used to mean ‘finally’, or ‘at last’. It will usually come at the beginning of a sentence.
Finally it has arrived in Japan!!!
The Dragons have finally won!
may be seen equally as often with or without kanji. When compared to 到頭（とうとう）, ついに is slightly more formal.
Finally it is your last day. Thank you for everything up until now.
It's finally your last day. Thank you for everything up until now.
The kanji 遂（つい） has a meaning similar to ‘to get (something) over with’. Due to this, ついに will most often be used to highlight things that have finally happened after a significant period of time, or a long course of events. It will not be used to express things that do not require time or effort.
You finally married!? Congrats!
I finally threw away the bag I bought yesterday.