Diogenes Laertius, 6.63, on Diogenes the Cynic (4th Century BCE)
“When asked where he was from, he said “I am a world-citizen.”
ἐρωτηθεὶς πόθεν εἴη, “κοσμοπολίτης,” ἔφη.
Cicero is one of the earliest sources attributing the sentiment to Socrates.
Cicero, Tusculan Disputations 5.108
“Socrates, when he was asked what state was his, used to say “the world”. For he judged himself an inhabitant and citizen of the whole world.”
Socrates cum rogaretur, cujatem se esse diceret, Mundanum, inquit. Totius enim mundi se incolam et civem arbitrabatur.”
Seneca, Epictetus, and Marcus Aurelius articulate different versions of what becomes a central part of Stoic philosophy.
Seneca, De vita beata, 20.5
“I know that my country is the world and that the gods are guardians, those judges of my deeds and words above and beyond me.”
Patriam meam esse mundum sciam et praesides deos, hos supra circaque me stare factorum dictorumque censores.
Seneca, De Otio, 4.1
“We encounter two republics with our mind–one is great and truly public, by which gods and men are contained and in which we may not gaze upon this corner or that one, but we measure the boundaries of our state with the sun; the other we enter by the fact of being born. This will be the state of Athens or Carthage or of any other city at all. It does not extend to all people but to certain ones. Some people serve the good of both republics at the same time, the greater and the lesser, some serve only the lesser or only the greater.”
Duas res publicas animo complectamur, alteram magnam et vere publicam, qua dii atque homines continentur, in qua non ad hunc angulum respicimus aut ad illum, sed terminos civitatis nostrae cum sole metimur; alteram, cui nos adscripsit condicio nascendi. Haec aut Atheniensium erit aut Carthaginiensium,aut alterius alicuius urbis, quae non ad omnis pertineat homines sed ad certos. Quidam eodem tempore utrique rei publicae dant operam, maiori minorique, quidam tantum minori, quidam tantum maiori.
Epictetus, Dissertationes 1.9.1
“If what is said about the kinship of humans and god by the philosopher is true, what is left for all people other than that advice of Socrates never to say when someone asks where you are from that you are Athenian or Corinthian but that you are a citizen of the world?”
εἰ ταῦτά ἐστιν ἀληθῆ τὰ περὶ τῆς συγγενείας τοῦ θεοῦ καὶ ἀνθρώπων λεγόμενα ὑπὸ τῶν φιλοσόφων, τί ἄλλο ἀπολείπεται τοῖς ἀνθρώποις ἢ τὸ τοῦ Σωκράτους, μηδέποτε πρὸς τὸν πυθόμενον ποδαπός ἐστιν εἰπεῖν ὅτι Ἀθηναῖος ἢ Κορίνθιος, ἀλλ᾽ ὅτι κόσμιος;
Marcus Aurelius, Meditations 3.11
“Nothing is as productive of an expansive mind than to consider truly and as completely as possibly everything you encounter in life and always to look at things so that you realize what the nature of the universe is, what each thing is used for, and what worth it has in relation to the whole, and how it relates to man, who is a citizen of the highest city, within which the rest of the cities are like houses. Think: what is it, and where is it from, and how long has it endured which now makes this impact on me.
And: what are the demands of virtue from me because of it? Gentleness, bravery, fidelity, simplicity, self-sufficiency and others. This is why at every opportunity we must say that this comes from god, this is according to the serendipity and spinning of allotment and this is from the same chance, while this is from the same character and family in common, even when one is ignore about what is his because of nature. But I am not ignorant. This is why I treat each person according to the natural law of the commonwealth, kindly and justly, just as at the same time, when dealing with indifferent things, I try to assign them their true value.”
οὐδὲν γὰρ οὕτως μεγαλοφροσύνης ποιητικόν, ὡς τὸ ἐλέγχειν ὁδῷ καὶ ἀληθείᾳ ἕκαστον τῶν τῷ βίῳ ὑποπιπτόντων δύνασθαι καὶ τὸ ἀεὶ οὕτως εἰς αὐτὰ ὁρᾶν, ὥστε συνεπιβάλλειν ὁποίῳ τινὶ τῷ κόσμῳ ὁποίαν τινὰ τοῦτο χρείαν παρεχόμενον τίνα μὲν ἔχει ἀξίαν ὡς πρὸς τὸ ὅλον, τίνα δὲ ὡς πρὸς τὸν ἄνθρωπον, πολίτην ὄντα πόλεως τῆς ἀνωτάτης, ἧς αἱ λοιπαὶ πόλεις ὥσπερ οἰκίαι εἰσίν: τί ἐστὶ καὶ ἐκ τίνων συγκέκριται καὶ πόσον χρόνον πέφυκε παραμένειν τοῦτο τὸ τὴν φαντασίαν μοι νῦν ποιοῦν καὶ τίνος ἀρετῆς πρὸς αὐτὸ χρεία, οἷον ἡμερότητος, ἀνδρείας,  πίστεως, ἀφελείας, αὐταρκείας, τῶν λοιπῶν, διὸ δεῖ ἐφ̓ ἑκάστου λέγειν: τοῦτο μὲν παρὰ θεοῦ ἥκει, τοῦτο δὲ κατὰ τὴν σύλληξιν καὶ τὴν συμμηρυομένην σύγκλωσιν καὶ τὴν τοιαύτην σύντευξίν τε καὶ τύχην, τοῦτο δὲ παρὰ τοῦ συμφύλου καὶ συγγενοῦς καὶ κοινωνοῦ, ἀγνοοῦντος μέντοι ὅ τι αὐτῷ κατὰ φύσιν ἐστίν. ἀλλ̓ ἐγὼ οὐκ ἀγνοῶ: διὰ τοῦτο χρῶμαι αὐτῷ κατὰ τὸν τῆς κοινωνίας φυσικὸν νόμον εὔνως καὶ δικαίως, ἅμα μέντοι τοῦ κατ̓ ἀξίαν ἐν τοῖς μέσοις συστοχάζομαι.
Marcus Aurelius, Meditations 4.1
“If the power of thought is common then our reason is also shared, through which we are rational beings. If this is true, then we also share the assignment of what to do or not to do according to reason. If that is true, than law is shared. If this is the case, we are fellow citizens. And if that is true, we shared some state. If we share a state, the world resembles a city. For what other state could claim to contain the whole human race?…”
Εἰ τὸ νοερὸν ἡμῖν κοινόν, καὶ ὁ λόγος, καθ᾽ ὃν λογικοί ἐσμεν, κοινός: εἰ τοῦτο, καὶ ὁ προστακτικὸς τῶν ποιητέων ἢ μὴ λόγος κοινός: εἰ τοῦτο, καὶ ὁ νόμος κοινός: εἰ τοῦτο, πολῖταί ἐσμεν: εἰ τοῦτο, πολιτεύματός τινος μετέχομεν: εἰ τοῦτο, ὁ κόσμος ὡσανεὶ πόλις ἐστί: τίνος γὰρ ἄλλου φήσει τις τὸ τῶν ἀνθρώπων πᾶν γένος κοινοῦ πολιτεύματος μετέχειν;.
A recent addition: