Golding, 23, made only one appearance for Rhinos in 2019, scoring a brace of tries in a Coral Challenge Cup win over Workington Town.
He spent most of the season with Rhinos' dual-registration partners Featherstone Rovers and was in their team which lost at Toronto Wolfpack in the Championship Grand Final.
Golding made his Rhinos debut in 2014 and scored 14 tries and 14 goals in 63 appearances, 50 of those in the starting side.
"The main thing for me was an opportunity to play in Super League and be able to compete at the highest level for this historic club," Golding said.
"I'm just trying to be the best person that I can be - I'm here to learn and I've spoken to the coaching staff and I believe that they're the right people to bring out the best in me."
He added: "I like to defend, I like the defensive side of the game and under Ryan Carr at Featherstone I feel like I've developed my offensive side and I'd like to be able to test myself at Super League level."
"I can't wait to get going, get training and meet all the lads and understand the differences in the clubs."
Rhinos director of rugby Kevin Sinfield said: "Ashton had three years left on his contract with us, but we felt it was fair to let him have the opportunity to leave the club to give himself the chance to become a starting full back at another Super League club.
"Ashton has been a brilliant player for us and he is a great character to have around the club and the way he conducts himself on and off the field makes him the perfect role model.
“We would like to thank Ashton for all everything he has given to the Rhinos and he leaves with our best wishes for the future.”
Giants coach Simon Woolford reckons Golding will make a major impact next season.
"I've watched him quite a bit this year and he's been a stand out at Featherstone and was key to their success this year," he said.
"He does a really good job defensively which is really important in a full-back.
"He's very good with the defensive side of things, he puts his body on the line and his effort is first class.
"From an attacking point of view, he's very fast, his passing game is something that has improved from the first time I've watched him and that'll be something we'll look to keep improving.
"He has got a level head, he's professional and he works hard and these are all things that we're looking for in recruits to Huddersfield Giants in 2020."