Auckland-born Quinn, 22, holds a UK passport and will not therefore count as an overseas player.
He is the first signing by the county since Thursday's appointment of former England paceman Chris Silverwood as head coach.
"Matt is a tall, fast bowler who can swing the ball. We've made no secret of the fact we want to bolster the bowling attack," said Silverwood.
"Having looked at Matt play, alongside his record in New Zealand, he's got a good pedigree."
Essex have had quite an overhaul since the appointment of former captain Ronnie Irani as their new cricket committee chairman.
England one-day international Reece Topley has joined Hampshire, while former skipper Mark Pettini has moved to Leicestershire and former England spinner Monty Panesar, Greg Smith, Matt Salisbury and Saf Imtiaz were all released at the end of last season.
But slow left-arm spinner Aron Nijjar and young fast bowler Aaron Beard have both signed their first professional contracts, while England all-rounder Ravi Bopara, opening batsman Jaik Mickleburgh, limited-overs captain Ryan ten Doeschate and England Under-19 all-rounder Callum Taylor have all agreed new deals.

Media playback is not supported on this device
Champion jockey AP McCoy was denied a fairytale Aintree farewell, finishing fifth on favourite Shutthefrontdoor.
Aspell, who won in 2014 aboard Pineau De Re, steered his 25-1 shot to the front three fences from home and then held off the challenge of Saint Are to win by a length and three-quarters.
Monbeg Dude finished third and Alvarado came in fourth.
Aspell, 38, becomes the first jockey since Brian Fletcher on Red Rum in 1973 and 1974 to win back-to-back Nationals, while it was a third success for 79-year-old owner Trevor Hemmings, who has previously won with Hedgehunter and Ballabriggs.
Aspell said: "It was wonderful and we will certainly celebrate tonight. I asked some big questions, but he dug deep.
"We really refreshed and recharged his battery and I tried to conserve energy. He is all heart. All season, he has had hard races. Win lose or draw, that's the best ride I have had in the National. I just hoped his battery life lasted out and it did."
McCoy appeared well placed in the latter stages, but Shutthefrontdoor tired badly from the elbow.
"I thought from the third-last fence I was running on empty," McCoy said.
"I will miss riding horses and races like that. I thought for a long way he could win. It was my last National but was a very enjoyable one."
The Northern Irishman had said he would retire immediately if he had won, but the 40-year-old could now race on until the Sandown meeting at the end of April.
Winning trainer Oliver Sherwood was in tears after his decision to run Many Clouds was vindicated.
The eight-year-old was a disappointing sixth in last month's Cheltenham Gold Cup after winning the Hennessy Gold Cup at Newbury in November and scoring at Cheltenham in January.
Many Clouds becomes the youngest winner of the National since Bindaree in 2002 and at 11st 9lb, the heaviest winner since Red Rum.
He also won £561,300 for Hemmings out of a total prize fund of £1m.
About 72,000 spectators turned out on a sunny day at Aintree to watch the 168th running of the National.
McCoy had been strongly backed in the lead-up to the race - with more money wagered on this National than any other horse race - and bookmakers had feared a £50m pay-out if he had claimed his second victory over the 30 National fences.
Nina Carberry, the only female jockey in the race, finished 16th on First Lieutenant.
Balthazar King, one of the favourites, had a heavy fall at the Canal Turn and was taken to University of Liverpool Equine Hospital (Leahurst) for further assessment.
Top six: 1. Many Clouds (25-1) 2. Saint Are (25-1) 3. Monbeg Dude (40-1) 4. Alvarado (20-1) 5. Shutthefrontdoor (6-1 fav) 6. Royale Knight (25-1).
Nineteen of 39 starters finished - click here for the full finishing order.
Essex have signed New Zealand A fast bowler Matt Quinn on a three-year deal.
[NEXT_CONCEPT]
Many Clouds won the 2015 Grand National to give jockey Leighton Aspell his second consecutive victory in the race.