Hose, 24, played 31 games for Somerset, having joined them in 2015, making his maiden one-day hundred in May.
He also made a match-winning 59 off just 28 balls in Somerset’s T20 Blast victory over Middlesex on 16 July.
“It’s a fantastic opportunity at an exciting time for the club. I now just need to work hard, score runs and earn a first-team place,” Hose told BBC WM.
“It was hard leaving Somerset but I went with my gut feeling. You just get the idea that this club is building something here.”