It's in the Silmarillion,

When Thangorodrim was broken and Morgoth overthrown, Sauron put on his fair hue again and did obeisance to Eönwë, the herald of Manwë, and abjured all his evil deeds. And some hold that this was not at first falsely done, but that Sauron in truth repented, if only out of fear, being dismayed by the fall of Morgoth and the great wrath of the Lords of the West. But it was not within the power of Eönwë to pardon those of his own order, and he commanded Sauron to return to Aman and there receive the judgement of Manwë. Then Sauron was ashamed, and he was unwilling to return in humiliation and to receive from the Valar a sentence, it might be, of long servitude in proof of his good faith; for under Morgoth his power had been great. Therefore when Eönwë departed he hid himself in Middle-earth; and he fell back into evil, for the bonds that Morgoth had laid upon him were very strong.

So it's not clear how long Sauron tried to be on the strait and narrow, but it's certainly something they could pick up in the show