Gaskell, 26, started his career with St Helens before joining the Bulls in 2013.
"To be back in Super League is a great feeling and to be given this chance by the Giants is pleasing," he told the club website.
"I've had a short time here and it's good to get that training under my belt."
Huddersfield Giants have signed Bradford Bulls stand-off Lee Gaskell on a four-year deal.