Question: I admit it has been years since reading LOTR but I always thought Strider wasn't revealed as the king until Return of the King.

Is this correct?

Answer: 
I'm not entirely clear on what you mean by "revealed", but he's announced as the *rightful* king (i.e. the heir of Isildur) in *Fellowship*:

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> 'And here in the house of Elrond more shall be made clear to you' said Aragorn, standing up. He cast his sword upon the table that stood before Elrond, and the blade was in two pieces. 'Here is the Sword that was Broken!' he said.
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> 'And who are you, and what have you to do with Minas Tirith?' asked Boromir, looking in wonder at the lean face of the Ranger and his weather-stained cloak.
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> 'He is Aragorn son of Arathorn,' said Elrond; 'and he is descended through many fathers from Isildur Elendil's son of Minas Ithil. He is the Chief of the Dúnedain in the North, and few are now left of that folk.'
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> *Fellowship of the Ring* Book II Chapter 2: "The Council of Elrond"
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And near the end of the book (emphasis mine):

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> 'Fear not!' said a strange voice behind [Frodo]. Frodo turned and saw Strider, and yet not Strider; for the weatherworn Ranger was no longer there. In the stern sat Aragorn son of Arathorn, proud and erect, guiding the boat with skilful strokes; his hood was cast back, and his dark hair was blowing in the wind, a light was in his eyes: **a king returning from exile to his own land**.
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> *Fellowship of the Ring* Book II Chapter 9: "The Great River"
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That he eventually *becomes* king is also spoiled in *Fellowship*, in the prologue (emphasis mine):

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> That book was a copy, made at the request of **King Elessar**, of the Red Book of the Periannath, and was brought to him by the Thain Peregrin when he retired to Gondor in IV 64.
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> *Fellowship of the Ring* Prologue 5: "Note on the Shire Records"
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Later in the book, Elessar is announced as another name for Aragorn (emphasis mine):

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> 'Yet maybe this will lighten your heart,' said Galadriel; 'for it was left in my care to be given to you, should you pass through this land.' Then she lifted from her lap a great stone of a clear green, set in a silver brooch that was wrought in the likeness of an eagle with outspread wings; and as she held it up the gem flashed like the sun shining through the leaves of spring. 'This stone I gave to Celebrían my daughter, and she to hers; and now it comes to you as a token of hope. **In this hour take the name that was foretold for you, Elessar, the Elfstone of the house of Elendil!**'
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> *Fellowship of the Ring* Book II Chapter 8: "Farewell to Lórien"
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From virtually the moment Strider is introduced, in Bree, he is proclaimed the subject of Bilbo's poem in Gandalf's unsent letter, which says the broken sword (and which Strider shows the hobbits) shall be renewed and the crownless shall be king. 2 + 2 = 4 and Strider, holder of the broken sword, is none other than Isildur's heir.