As long as we want to convey that we've been talked into something, we may do it with persuadeo.

One must be careful though: the expressions mihi persuasum est and persuasum habeo usually mean "I am convinced that...", not "I've been convinced": see here. However, Seneca does start one of his letters to Lucilius with

Quid non potest mihi persuaderi, cui persuasum est ut navigarem?

 

What may I not be persuaded to do, when I have been persuaded to sail?

In order to say "You've changed my mind!" we may thus either say (Mihi) persuasum est! - and after all, the "I'm convinced" nuance is excluded by the fact that we didn't originally agree - or Mihi persuasisti!: in the Digesta Iustiniani we have

[...], falso mihi persuasisti, tamquam eam pecuniam servo meo aut procuratori solvisses;

 

[...], you falsely persuaded me that you would pay that money to my slave or my procurator;

As long as we want to convey that we've been talked into something, we may do it with persuadeo.

One must be careful though: the expressions mihi persuasum est and persuasum habeo usually mean "I am convinced that...", not "I've been convinced": see here. However, Seneca does start one of his letters to Lucilius with

Quid non potest mihi persuaderi, cui persuasum est ut navigarem?

What may I not be persuaded to do, when I have been persuaded to sail?

In order to say "You've changed my mind!" we may thus either say (Mihi) persuasum est! - and after all, the "I'm convinced" nuance is excluded by the fact that we didn't originally agree - or Mihi persuasisti!: in the Digesta Iustiniani we have

[...], falso mihi persuasisti, tamquam eam pecuniam servo meo aut procuratori solvisses;

[...], you falsely persuaded me that you would pay that money to my slave or my procurator;