The man and woman left Auckland on Saturday. It is understood they chartered a plane based in Hawke's Bay which travelled to Auckland, collected them and flew directly to Wānaka.
Flight tracking data shows they landed in Wānaka just before midday. Police were later alerted and began an investigation.
The man is the founder of a company that deals in cryptocurrency investment and digital asset management.
A source said the couple appeared to have all the relevant documentation that would allow them to leave Auckland and travel to Wānaka.
In a statement on Thursday afternoon police said they had reviewed the business travel documentation and were satisfied the pair were permitted to travel to certain parts of New Zealand for work purposes.
"Police are satisfied there was no breach of the Health Order, and now consider the matter closed and any further information or clarification on their travel should be referred to MBIE [Ministry of Business, Innovation and Employment]."
The source earlier urged people to remain calm about the situation until all the facts were established. They said online abuse directed at the pair may be completely unfounded.
"People are literally sending death threats, it's disgusting."
The pair chartered the flight through Skyline Aviation Limited, based in Napier.
A lawyer acting for the entrepreneur, whom The New Zealand Herald has chosen not to name at this stage, defended the travel.
He told Stuff his clients lived in the Otago region and their travel was for "legitimate business reasons".
An MBIE spokesperson said the entrepreneur and his employee held the relevant business travel documentation required to cross alert level boundaries.
Lawyer, equestrian 'deeply sorry' for Wānaka trip
The pair's trip was a "completely different situation" to another case of Aucklanders leaving Alert Level 4 and travelling to Wānaka, the source told the Herald.
William Willis (35) whose mother is District Court Judge Mary-Beth Sharp, and 26-year-old lawyer Hannah Rawnsley were dobbed in after arriving at a holiday home in Wanaka last week.
The couple left Auckland on Thursday, September 9, using essential worker exemptions to cross the boundary and drive to Hamilton Airport before taking a commercial flight to Queenstown via Wellington and hired a car to drive to Wānaka, police said.
A tipster alerted police to the trip through the Covid-19 online compliance tool and the couple was approached on Saturday afternoon, police said.
The couple has since returned to Auckland and, after abandoning a bid for name suppression, issued a statement apologising for their alleged breach.
Police have indicated Willis and Rawnsley will likely face charges - but there might be some delay in getting the case before the courts due to court restrictions resulting from the ongoing lockdown.
"The decision that we took to travel to Wānaka last week was completely irresponsible and inexcusable," the couple's statement said.
"We are deeply sorry for our actions and would like to unreservedly apologise to the Wānaka community, and to all the people of Aotearoa New Zealand, for what we did.
"We can confirm that as part of routine testing for essential workers when crossing the Auckland border, we both received negative Covid-19 tests prior to undertaking the travel, and on our subsequent return to Auckland. We can also confirm we were not considered close contacts nor had we had visited any locations of interest.
"... We understand that strict compliance is required to stamp out Covid-19 from our country. We have let everyone down with our actions, and we wholeheartedly apologise."
Auckland remains under alert level 4 - the most stringent Covid-19 lockdown - until at least next week, while the rest of New Zealand is in alert level 2.
- additional reporting ODT Online
