The 18-year-old has moved to the John Smith's Stadium on a two-year deal for an undisclosed fee.
Roberts made five Super League appearances in two years for Bradford, though he spent the second half of last season on the sidelines with a broken leg.
"Bradford offered me a deal to stay when I regained fitness from injury but I wanted to stay in the Super League competition if at all possible after our relegation," he is quoted as saying by Sky Sports News.
"The Giants expressed interest and as I live really close and played amateur rugby with a few of the boys there I know how good a setup it is and I am joining a top-four club."
Huddersfield reached the preliminary semi-finals of last season's Super League playoffs before they were beaten by Catalans Dragons.