The 23-year-old former England Under-19 international had a trial spell with Kent at the start of last season and featured for their second XI in 2014.
"I'm delighted to be rejoining Kent on a more permanent basis," he said.
"I really enjoyed my time at the beginning of last year. Hopefully I can use this opportunity to push on and secure a regular first-team spot."
Zimbabwe-born Rouse has played five first-class matches since making his debut for Hampshire in 2013, as well as 10 in the limited-overs formats.
Kent have signed former Hampshire and Gloucestershire wicketkeeper-batsman Adam Rouse on a two-year deal.