The phrase "to finalise a move" means to complete or finish all the necessary steps in order to achieve a particular change or transition. Full definition
According to Sport, as translated by Sport Witness, the Brazilian's reps met Barca chiefs this week to strike a deal and came out of their meeting happy, with the player's contract apparently sorted and with growing confidence that he can finalise his move in the first week of January. (caughtoffside.com)
Chelsea were the first Premier League club of the day to have a deal confirmed, with midfielder Kevin de Bruyne finalising his move from Genk, but returning to Belgium on loan for the rest of the season. (metro.co.uk)
They made the move but Chelsea finalised the move... That's the difference. (justarsenal.com)