The 24-year-old, who has been capped twice, will make the move in the summer from Rabodirect Pro 12 outfit Ulster.
Whitten graduated through the Ulster academy set-up and has gone on to make 61 appearances for the Ravenhill side.
However he is relishing the chance to test himself in the Aviva Premiership with the Chiefs.
"Obviously I'm delighted with the move," he said. "It's going to be a new challenge in a tough environment for me, but it's one I am very much looking forward too.
"I was very impressed with the facilities at Exeter when I came over and also by all the people who seemed very friendly and made me feel very welcome.
"Testing myself in the Premiership is going to be great because it's a very tough league and every week the challenge is there for you to take on.
"It is always sad to move on from a club, especially because I've had a lot of good times at Ulster. But I see this as a new chapter for me in my career and I want to try something different. You can see Exeter are a club with real ambition and are moving in the right direction.
"Speaking with both Rob (Baxter) and Ali (Hepher) it was all very positive and I like what they had to say. Hopefully I can bring something to the squad and help finish off some of the opportunities the team create."
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