The Polish people "never succumbed to tyranny", Mr Johnson said.
"Today Poland lives and thrives in the heart of Europe, just as Churchill foretold," the prime minister said.
He added that the UK has stood with Poland "in times of triumph and tragedy".
As well as Ms Merkel, German President Frank-Walter Steinmeier attended the events where he asked Poland's forgiveness for Nazi "tyranny".
Mr Steinmeier also apologised for the "horrific war" unleashed by Germany.
"This war was a German crime," he said in a speech.
As well as world leaders, veterans also attended the event which saw military parades.
was snubbed by the organisers of the anniversary event and Polish president Andrzej Duda used his speech to denounce aggression shown towards Georgia and Ukraine and the "imperialist tendencies" being displayed in Europe.
Following Hitler’s invasion of Poland on September 1, 1939, British prime minister Neville Chamberlain admitted to the nation in a sombre radio address that his "long struggle to win peace" had failed.
Hours later, France issued its own ultimatum to Germany, setting in train the Second World War.
It was a conflict that lasted nearly six years and cost around 50 million lives.
Chamberlain made his famous radio address from the Cabinet room in 10 Downing Street.
He said: "This morning the British ambassador in Berlin handed the German Government a final note stating that, unless we heard from them by 11 o’clock that they were prepared at once to withdraw their troops from Poland, a state of war would exist between us.
"I have to tell you now that no such undertaking has been received, and that consequently this country is at war with Germany.
"You can imagine what a bitter blow it is to me that all my long struggle to win peace has failed.
"Yet I cannot believe that there is anything more or anything different that I could have done, and that would have been more successful.”
He concluded his broadcast: "Now may God bless you all and may He defend the right.
"For it is evil things that we shall be fighting against – brute force, bad faith, injustice, oppression, and persecution. And against them I am certain that the right will prevail."
A year earlier, Chamberlain had returned to London from talks in Munich clutching an agreement signed by Hitler that he said meant "peace for our time".
But the German leader continued his aggression in Europe, culminating in the invasion of Poland.
Ray Smith, from Northampton, said he was 14 or 15 when Chamberlain made the declaration.
The 94-year-old said the gravitas of it all did not sink in, adding: "I don’t suppose at that age you realise quite what it was."
Joining the Royal Navy at 17, a year later he took part in D-Day - serving on board HMS Middleton, the ship that supported troops landing on Sword beach.
With no time to be worried or scared, he said even though it was the summer it was "really rough weather", with equipment and tanks initially being dropped too far out.
"When the ramps went down and they (the troops) jumped in, they just vanished with all of the gear on," he said.
Describing the waters of Normandy, Mr Smith said there were "bodies floating everywhere".
When asked what advice he has for future generations, the father-of-two and grandfather-of-three said: "I just hope it never comes to a war like that."
There are no official major UK events planned to commemorate the 80th anniversary of Britain’s declaration of war on September 3, after which the country went on to suffer an estimated 400,000 military and civilian casualties.