Let's get the Greek text out...
οὐχ ὑμεῖς με ἐξελέξασθε, ἀλλʼ ἐγὼ ἐξελεξάμην ὑμᾶς
As for the difference in the listed lexeme in the lexicons (and in this case, concordance), the relationship between the forms is active vs. middle. I haven't looked through the history of the verb to say for sure, but it appears that it has undergone a shift from being an active verb to being a middle-only verb at some point in the Koine period. The active form is getting pretty rare in the Koine period (36 search hits), at least in the texts I searched in Logos (NT, LXX, Josephus, Philo, Apostolic Fathers, & OT Pseudepigrapha), while the middle form is quite common (233 search hits).
One would have to look through some classical texts to know for sure. Minimally, LSJ lists the active form ἐκλέγω...
Language Editor, Logos Bible Software
Linguistics Consultant, Occasional Photographer, & Constant Student