If it is true that Jewish brides wear the wedding ring on the right hand, why is this so?

The ring is placed on the bride and groom's right index finger only in the ceremony, and then each moves the ring over to the left hand, where it remains.

The reason for this is twofold:
1 - There is a vein that runs from the right index finger to the heart, therefore, when the rings touch the right ring finger, they are essentially connected to the heart.

2 - marriage is a free will act of commitment, so the bride and groom each freely move the ring from the right index to the left ring as a sign of accepting the ring in marriage.

Cantor Debbi Ballard
www.mypersonalcantor.com

The ring is put on the right hand because the right hand is a symbol
of strength. Everything they want to bless is taken by their right hands.

I noticed something more when I searched this question on about.com. Rabbi Lerner, in answering it, noted that the ring first goes on the index finger of the bride's right hand and is moved later to its customary position.

The placement of the ring has more to do with religious custom and tradition (from Judaism or Christianity, as appropriate) than any obligation. In the words of Rabbi Lerner: "Fidelity, which is the meaning of the ring, has less to do with the heart than a strong conscience and sense of integrity. Thus, any finger will do.

judaism.about.com/library/3_askrabbi_c/bl_weddingring.htm

A traditional reason to wear wedding rings on the right hand stems from Roman custom and biblical references. The Latin word for left is "sinister", which in addition to this sense also has the same senses as the English word. The Latin word for right is "dexter", a word that evolved into "dexterity". Hence, the left hand had a negative connotation and the right a good one. For the same reason, an oath is sworn while raising the right hand.

Most American Jewish brides wear their wedding ring on their left ring finger.