Dagg, who has been a stand-out for the Highlanders at fullback for the past two years, and who was picked in the All Blacks this year, announced yesterday he had signed with the Crusaders for the next two seasons.
Crusaders coach Todd Blackadder said Dagg was a special talent and was sure he would fit in very well.
Dagg had been openly courted by the franchise.
The 22-year-old Hawkes Bay product could not be contacted yesterday, and his agent, Simon Porter, said Dagg did not want to say anything about the switch. Porter declined further comment.
Highlanders chief executive Richard Reid said it was obviously disappointing to lose a player of Dagg's calibre but it was the reality of professional sport.
He said the Crusaders had to work within a budget, as every franchise did, and they were not stock-piling talent.
Franchise direct contracting, introduced for next season, was supposed to lead to the spreading-out of talent across the five New Zealand franchises, as teams would be forced to pay more for All Blacks and other talented players.
But this does not appear to have happened in the Crusaders' case, as they have signed the likes of Sonny Bill Williams and Dagg in the past couple of months.
Reid said the Highlanders had made a good offer to the fullback but Dagg had wanted to go to the Crusaders.
"We were keen to keep Izzy but he is a young man with ambitions, the Crusaders are a good franchise, his good mate Zac Guildford is with the team, so he has decided to move on. It is a pity but it is a chance for someone else."
New Highlanders coach Jamie Joseph had talked to Dagg about staying with the team, Reid said.
Developing a player who then moved on to another side was just professional sport, he said.
"Look at the Manchester Uniteds, the Real Madrids of this world, they get their man. It is just the way it is. The bigger fish in every league get their man.
"But if we can get the team right on the field, play a bit better, win a few more games, it becomes easier to get them [players]."
Southland fullback Robbie Robinson looms as Dagg's replacement.
Reid said the franchise had been working hard on recruitment and was due to make some announcements on players in the next few weeks.
Highlanders lock Hayden Triggs revealed this week he was eying an offer to move to the Chiefs next year.
There has been speculation Adam Thomson will follow Dagg to the Crusaders, and Reid said Joseph would be addressing that situation in the next couple of weeks.
There has also been speculation Canterbury first five-eighth Colin Slade will head to the Highlanders to fill the troublesome No 10 jersey.
He has been playing there for Canterbury this season after directions from the All Black coaches to move into the position.
Reid said he had heard the talk about Slade coming south but nothing could be confirmed.