The 33-year-old will also wear the armband for Evesham, who play in Southern League Division One South.
It ends a long association with the Yeltz, who were relegated from the Southern Central Premier Division last season.
Manager Paul Smith paid tribute to Bargoli, saying: "A brilliant servant for Halesowen who has conducted himself impeccably since I arrived.
"An old school attitude that unfortunately is lost with the majority of younger players these days. I wish you all the very best going forward Brags."
Evesham United manager Carl Abbott said: "Absolutely over the moon that Danny has signed.
"He is a soldier on the pitch, an absolute warrior. Getting the right leader for the group was of paramount importance.
"In the dressing room he is an inspiration, he will drive the team and represent us, the management, on the pitch.
"I’ve huge respect for Danny, he’s been a top top player for many years now at step three. Really happy he is in our camp."