The 26-year-old France forward had been heavily linked with Manchester United, and said last month there was a "6/10" chance he could move to Old Trafford this summer.
But he agreed to stay at Atletico after the club had a transfer ban upheld.
"The first thing I want to do is apologise to people who misunderstood my statements," Griezmann said.
"Since I have arrived, I have given everything for my club, my colleagues and my coaching staff."
Atletico cannot sign anyone until January after failing in an appeal against a ban imposed in July 2016 for breaching Fifa rules over the signing of youth players.
Griezmann, capped 41 times, scored 26 goals in 2016-17 as Atletico finished third in La Liga behind Real Madrid and Barcelona.
He was named the third best player in the world, behind Cristiano Ronaldo and Lionel Messi, at the Ballon d'Or ceremony in January.
Griezmann, who played in France's 2-1 defeat by Sweden in World Cup qualifying on Friday, is in the squad to face England in a friendly on Tuesday.
BBC World Service's John Bennett:
For me, the most interesting piece of information about Antoine Griezmann's new contract is the release clause. The club have confirmed that it stays the same, at 100 m euros, that's around £88m.
So despite the fact that 2022 is printed on the contract, this feels very much like the Frenchman will give Atletico Madrid one more year before making the big money move we all expected him to make this summer.
For now though the Atletico fans will be delighted by Griezmann's loyalty. He said it would be a "dirty move" to leave the club in their hour of need and he has kept his word.

New business levels also "stagnated" during October and volumes of incomplete work dropped.
The Bank of Scotland PMI survey showed companies added to their payrolls for the third successive month.
That was despite firms facing the sharpest increase in input costs since September 2011.
A further rise in output charges was reported, although the rate of inflation was weaker than that for input costs.
Seasonally-adjusted figures showed Scotland's private sector grew for a second successive month.
The increase in output was spread across manufacturers and service providers, with both reporting "marginal growth" in business activity levels.
The PMI panel members said companies' cost prices increased at the sharpest rate for more than five years as a consequence of a drop in the strength of the pound.
Nick Laird, the regional managing director of Bank of Scotland Commercial Banking, said: "Output for Scottish private sector companies continued to show growth in October, albeit at a reduced rate weighed down by a combination of higher input prices and stagnating new business.
"The increasing cost burden is a cause for concern, with the rise in input costs growing at the quickest rate in just over five years attributed to the depreciation of Sterling.
"Encouragingly, workforce numbers rose for a third consecutive month. Yet with a further solid decline in backlogs of work recorded, we could see jobs growth come under pressure towards the end of the year."
Atletico Madrid's Antoine Griezmann has extended his contract by a year, with his new deal expiring in 2022.
[NEXT_CONCEPT]
The expansion of Scotland's private sector has slowed down while output growth has weakened, according to a report.