Wardle departs a week on from his try-scoring debut for England in the win over the Combined Nations All Stars at Warrington's Halliwell Jones Stadium.
The 23-year-old has been limited to six appearances for the Giants after falling behind Ricky Leutele and Leroy Cudjoe in the pecking order on his return from a 10-week lay-off.
Huddersfield-born King has World Cup aspirations of his own and, like Wardle, felt a change of scenery would improve his chances of claiming a place in Shaun Wane's squad.
The 25-year-old has scored 52 tries in 138 games for Warrington since making his debut in 2014, including seven in 13 Super League outings this season.
Huddersfield managing director Richard Thewlis said: “The deal came about very quickly yesterday and upon reflection is one that suits all parties at this stage of the season and one that both players wanted.
“We have two young men vying to catch the eye of Shaun Wane to play in the World Cup and want to be playing each and every week to give themselves the best opportunity to do so.
“Jake has only made six appearances to date this year for us and his management informed us that a fresh start was of interest to him to 'reboot' so to speak his season and a similar scenario could be applied to Toby who is keen to take up the challenge here for the remainder of the year."
Thewlis has raised the prospect of the swap deal becoming a permanent arrangement.
He added: “Toby, of course, is a Huddersfield lad hailing from Meltham well known to many of our squad and will join up with us as soon as practical, although not in time for tomorrow's game at Hull Kingston Rovers where Ian (Watson) has already selected his side and Jake was due to be a travelling reserve so it doesn’t impact on our work done during the week ahead of a critical game.
“All parties involved in this arrangement have said we’ll assess the longer-term situation after both players have had some time in their new environments as the deal only runs for this year.”