The Black and Whites tried to sign the 20-year-old Wests Tigers player before the season started to enable him to line up alongside major signings Gareth Ellis and Daniel Holdsworth, but the NRL club insisted he remained part of their plans under new coach Mick Potter.
Miller recently lost his place in the Tigers team, however, and has been released by the club.
Hull coach Peter Gentle said: "It's a timely acquisition for us in a position we have been looking to cover for some time now.
"Jacob is a player that has all the attributes to be a quality half-back and we feel can really benefit our side, as well as improving his own game."
Miller will be a straight replacement for fellow countryman Brett Seymour, who was released by Hull last month. He will continue to train in Australia until he receives his visa.
"I am really excited about the opportunity to play in Super League with Hull FC," Miller said.
"It looks like it's a great time to be joining Hull. They have a strong roster and what looks like a great stadium, so I can't wait to get over there and get started."
Miller, who began his career with Sydney Roosters, played a pivotal role in the Tigers' Under-20s Grand Final success in 2012 and represented the Junior Kangaroos.