Παῦλος ἀπόστολος Χριστοῦ Ἰησοῦ διὰ θελήματος θεοῦ καὶ Τιμόθεος ὁ ἀδελφὸς — Colossians 1:1Paul often refers his apostleship to the will of God. To wit:
1 Corinthians 1:1 Παῦλος κλητὸς ἀπόστολος Χριστοῦ Ἰησοῦ διὰ θελήματος θεοῦ καὶ Σωσθένης ὁ ἀδελφὸςI may discuss this more fully if we get to v. 9, but it's my settled conviction that Scripture teaches only two aspects to the will of God, and not three.
2 Corinthians 1:1 Παῦλος ἀπόστολος Χριστοῦ Ἰησοῦ διὰ θελήματος θεοῦ καὶ Τιμόθεος ὁ ἀδελφὸς τῇ ἐκκλησίᾳ τοῦ θεοῦ τῇ οὔσῃ ἐν Κορίνθῳ σὺν τοῖς ἁγίοις πᾶσιν τοῖς οὖσιν ἐν ὅλῃ τῇ Ἀχαΐᾳ,
Ephesians 1:1 Παῦλος ἀπόστολος Χριστοῦ Ἰησοῦ διὰ θελήματος θεοῦ τοῖς ἁγίοις τοῖς οὖσιν [ἐν Ἐφέσῳ] καὶ πιστοῖς ἐν Χριστῷ Ἰησοῦ,
2 Timothy 1:1 Παῦλος ἀπόστολος Χριστοῦ Ἰησοῦ διὰ θελήματος θεοῦ κατ᾽ ἐπαγγελίαν ζωῆς τῆς ἐν Χριστῷ Ἰησοῦ
By the range of expressions referring to God's will, Scripture only means God's sovereign will, which it is His responsibility to affect (i.e. Ephesians 1:11), or His revealed will, which it is our responsibility to fulfill (i.e. Romans 2:18). There is no third will of God referring to neither certainly decreed events, nor inerrantly and specially revealed directions, but to subjective, erring, and personal perceptions.
Having said that, I don't argue that it is always easy to tell which of the two is in mind.
In this case, however, while both elements are present, it is the former that is probably foremost in Paul's mind. Think of Galatians 1:1 — Παῦλος ἀπόστολος οὐκ ἀπ᾽ ἀνθρώπων οὐδὲ δι᾽ ἀνθρώπου ἀλλὰ διὰ Ἰησοῦ Χριστοῦ καὶ θεοῦ πατρὸς τοῦ ἐγείραντος αὐτὸν ἐκ νεκρῶν. Here, the stress is clearly on God's sovereign will and activity. Thus also the effectual call to be an apostle, in Romans 1:1's κλητὸς ἀπόστολος.
Now, necessarily, an apostle did receive direct and special revelation of God's will (cf. Galatians 1:11-12) . That was the nature of the office. But the phrase itself here probably means that God made Paul an apostle by sovereign appointment; the fact that it involved a special revelation is incidental to the phrase here, though essential to the office itself.
What the apostle clearly didn't mean was that, one day, in his quiet time with God, he felt a still, small voice, subtly urging him towards seeking apostleship. That isn't the way it happened. Paul didn't merely "feel moved" to be an apostle. God sovereignly willed Paul to be an apostle, so he was.