This is largely an out-of-universe answer.
Using odd sentence structure like this is much more common in antiquated English, for instance from the Renaissance. Specifically, poets would restructure their sentences so that the rhymes could work better. For instance, look at the first stanza of this John Milton poem, On the Morning of Christ's Nativity:
This is the month, and this the happy morn,|
Wherein the Son of Heav'n's eternal King,|
Of wedded Maid, and Virgin Mother born,|
Our great redemption from above did bring;|
For so the holy sages once did sing,|
That he our deadly forfeit should release,|
And with his Father work us a perpetual peace.
As you can see, a lot of the time the verb is at the end of the sentence/phrase. Aside from making it easier to rhyme, this choice was made to more closely resemble Latin. From this blog post:
In Latin, word order is flexible... the ancient Romans preferred that the verb be placed at the end of a sentence
Latin was used for many years in Europe as the language of science and religion, so if you wanted to sound smart or religious you could try to make your English follow Latin sentence structure.
In modern times, using this sentence structure often implies an association to an ancient order, or vast stores of knowledge, or a spiritual enlightenment. I think when it's invoked in Revenge of the Sith, it's meant to mark Palpatine's shift from a frail politician to a wise and powerful Sith lord.
It's possible there was originally a similar intention with Yoda, to make him sound like a fancy old Jedi, but after Empire his speech patterns lost most of their resemblance to English from any time period.