The 26-year-old Scotland full-back will move to Sandy Park on a two-year deal at the beginning of next season, bringing to an end his nine-year spell with Glasgow.
After confirming the move, Hogg told Exeter's official website: "I'm very excited about the move, it's a great opportunity for myself and my family.
"Like a lot of people, I've seen how the Chiefs have risen over the last few years and I am a big fan of the way they play their rugby.
"This is a decision that's taken a great deal of thought as I've loved my nine seasons at Glasgow Warriors.
"I said I would decide my next step for family and rugby reasons and feel now is the right time to gain new rugby experiences and push myself in different situations where I will be challenged and hopefully improve further."