It is said that the Buddha attained Nirvana after his death. But how do we know that it is true? Are there any physical signs to recognize?
There is no physical signs of that and we can not verify it. Probably only enlightened beings (such as other buddhas) can verify this, so until we are enlightened we can't.
Btw, he also attained Nirvana before his death too. So-called nirvana with remainder.
Nirvana is a loss of form. The "Nirvana with remainder" is an apparent loss of form. While the absolute Nirvana is the eternal fact that the form has always been an imputation, and such nuisances as birth and death can in no way affect this global situation.
When we die, we lose the form in the literal sense, and for Buddhas this is called Maha-Pari-Nirvana (the great and final loss of form). In other words, Maha-Pari-Nirvana is when the apparent Nirvana perfectly coincides with the absolute Nirvana.
"It is said that the Buddha attained Nirvana after his death. But how do we know that it is true? Are there any physical signs to recognize?"
Because Buddha attained "Nirvana with remainder" during his life, his death is parinirvana, by definition. No signs necessary.
Lord Buddha attained Nibbana under the Bodhi tree at the age of 35. He entered Parinibbana at the Mallas' Sala Grove, in Kusinara at the age of 80. We don't use the word 'death' as Nibbana is deathless. He fully experienced Nibbana from the day he attained enlightenment under the Bodhi tree. Those are just technical terms used to identify whether there's a remnant of the five aggregates or not. We use the term Sa-Upadisesa Nibbana to refer to the Buddha's Nibbana while he is still living and Anupadisesa Nibbana to refer to his Parinibbana.
This is not something that can be directly answered or rationalized through the way to find the answer is there. This is by walking the 8 fold path and getting deep penetrating insights through Vipassana, where by attaining at least the 1st stage of sainthood which would result in this doubt is broken as you have verified for your self.
A loose analogy can be it is difficult to describe a hidden city / exotic treasure chest you have not being there perfectly to someone else but you can be told the route to get there so you can get there and see for yourself. If the route leads you to the particular city you know that the person has gone there.