O'Connell, a third-round pick in 2008 out of San Diego State, appeared in two games in 2008 and completed four of six passes for 23 yards. He was listed as the third-string quarterback in 2008.
Hodel signed with New England as a free agent on March 10. He signed with Carolina as a rookie free agent in 2001 and was waived prior to the beginning of the season. He spent six weeks on the practice squad before signing with Arizona, where he spent the next seven seasons.
In addition to starter Tom Brady, the Patriots now have two quarterbacks on the roster: Andrew Walter and Brian Hoyer.