Redpath is in his second season in the role having initially joining the club as backs coach. Hogg has been at Kingsholm since 2006 having served as academy manager before taking up his current position.
"We've got an outstanding group of staff, from Carl right through to Barny Allen and Bob Stewart, and all their hard work has gone into what we've achieved so far this year," said Redpath.
"The performance so far has yielded a contract renewal for myself and Carl, and I'm delighted to stay here. I've thoroughly enjoyed it even though it's been tough.
"We're trying to build an old-fashioned club culture, I can't think of any better place to do that than at Gloucester, and three years gives us a good platform and the challenge now is to improve again for next year."