The 21-year-old, who can operate at right-back or in the centre of defence, is yet to make an appearance for Rovers since coming through their academy.
He has spent the last two seasons on loan, playing in Sky Bet League Two. In 2012/13, he made 53 appearances for Burton, and in 2013/14, O'Connor played 32 times for Torquay, who were relegated.
The Republic of Ireland youth international was sent off on the final day of the season for Torquay, so he will miss Argyle's first game against Cambridge. The first game he can play for his new club will be their Capital One Cup tie with Leyton Orient on August 12.