The 25-year-old is expected to leave Real Madrid before the end of the transfer window on Tuesday next week.
Fiorentina have had an agreement in place with Real Madrid over a loan deal and were in talks with the player to convince him to move to Italy.
Until Wednesday, the Spaniard was undecided over whether to join Fiorentina and Tottenham showed late interest in taking him to England.
But according to Sky Italia, Fiorentina have obtained the consent of the player over a switch to Serie A this summer.
Odriozola has been convinced by the arguments put forward by the Italian club and is ready to join them.
Fiorentina will now look to finalise the agreement with Real Madrid and take care of the fine print of the deal between the two clubs.
The Spaniard will soon travel to Italy once the two clubs finalised the agreement for his loan move.
It remains to be seen whether Tottenham will try to hijack the deal, but Odriozola appears Fiorentina bound.
