Smith, 22, has signed a four-and-a-half year deal with the Fartowners and comes straight into contention for Saturday’s crucial Super League game against Catalans in Perpignan as they seek to secure fourth place.
Mullally had already agreed to join Leeds Rhinos for 2016 but will play the rest of this season on loan at Belle Vue as Super League’s bottom club battle to stave off the threat of relegation.
Huddersfield managing director Richard Thewlis: “We have an excellent relationship with (chairman) Michael Carter at Wakefield and had agreed some time ago with him for Daniel Smith to become a Giant in 2016 and beyond.
“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.
“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’m sure our fans will look forward to Daniel putting a claret and gold shirt on in the near future.”
Yorkshireman Smith originally came through Leeds’s Academy without ever playing a first-team game. He headed out to Australia in 2013 where he featured with South Sydney’s Under-20s team before returning home to join Wakefield last season.
Giants host Trinity in their final regular round a week Sunday. Both players can play for their new clubs.