Singer-songwriter Lizzie Marvelly was among the passengers on the flight.
"All of a sudden two security officers boarded the aircraft and kind of made their way down to the middle and hauled off a passenger who looked strikingly like Bob Jones," Ms Marvelly said after arriving at Wellington Airport.
"And then the captain came out, after the gentleman had been escorted off the plane, just apologised and said they couldn't accept people on planes regardless of who they were, if they didn't comply with air crew."
Ms Marvelly said passengers seated around the property magnate "clapped and cheered" when he left.
She said the incident was "all very dramatic for a moment" and the flight was delayed for about 15 minutes.
Passenger Madeleine Wilson said everyone clapped and Sir Bob "just walked straight out".
Sue Barber from Pukerua Bay said "everybody around" Sir Bob applauded when security boarded to remove him.
She said the captain told passengers: "It doesn't matter who you are, how important you are, you must obey CAA regulations."
Fellow passenger Diana Raynes from Auckland said: "The pilot said he was breaking aviation rules and no matter who they are, they shouldn't be allowed to get away with it essentially."
Nathan Scott said "multiple stewardesses" had tried to get Sir Bob to acknowledge his role in an emergency, but it was to no avail.
"The stewardesses were extremely polite ... He was given every opportunity by multiple stewardesses just to say yes or if he didn't want to, to move to another seat and refused."
Mr Scott said he was astounded Sir Bob was later allowed to catch another flight, "reinforcing his right to cause trouble to others with no impact".
Sir Bob, 75, did not return a message left at his home this evening and earlier declined to talk to reporters at Wellington Airport, but reprimanded a TV journalist for not having good "manners."
Civil Aviation Authority spokesman Mike Richards said the pilot of the 10.35am flight asked Aviation Security (Avsec) to "de-plane" a passenger.
Mr Richards earlier confirmed the man was Sir Bob Jones and he would not face charges.
Arrests for such behaviour are uncommon. Last week, a rowdy Jetstar passenger was kicked off a plane about to leave Dunedin, banned from flying with the airline for 24 hours, but not charged.
Mr Richards said the passenger in today's incident was not following crew instructions during the important safety briefing. The pilot then said he did not want to carry him on the flight.
Sir Bob then "co-operated fully" with an Avsec officer.
"He was then met by an Air New Zealand duty manager who arranged for his travel on another Air New Zealand flight," Mr Richards said.
Avsec agreed with the cabin crew that Sir Bob should not be on the flight, he said.
"This is a timely reminder that, no matter how often you fly, it is critical that passengers pay attention to all instructions given by the crew on board an aircraft, even if they are familiar with the routine," Mr Richards added.
"The procedures are in place to ensure safe travel for all."
An Air New Zealand spokeswoman confirmed Avsec was called to flight NZ421 this morning to deal with a passenger who refused to follow crew instructions.
"The captain requested that Aviation Security remove the passenger from the flight, in line with civil aviation requirements," she said.
