Smith, 22, has signed a four-and-a-half-year deal with the Giants. He will be available for selection this weekend against Catalans Dragons.
Mullally agreed to join Wakefield on loan to facilitate the move. He is joining Leeds Rhinos next season.
“We have an excellent relationship with Michael Carter at Wakefield and had agreed some time ago with him for Daniel Smith to become a Giant in 2016 and beyond,” said Giants managing director Richard Thewlis.
“Wakefield approached us to talk about ideas for new faces for their squad and obviously we were keen to get Daniel into our environment as soon as possible, and with Anthony having decided to move on longer term from the club a deal was struck to the end of the year, which suited all.
“Anthony leaves with our very best wishes for the future and I am sure that our fans will look forward to Daniel putting a claret and gold shirt on in the near future.”