Origins of the phrase "Gentlemen: Yours to hand, and, In reply......."

In this context Yours means your letter, i.e., the letter you sent.

to hand means: within reach, accessible, at hand.
at hand means: within easy reach; near; close by

So the meaning would be:

• "I have received your letter and in reply to it..." ; or
• "I have your letter right here beside me (to hand, at hand), and in reply. . ."; or
• "I have your letter in hand, and I'm replying."

Credits:
Thanks to Peter Duncanson, Pat Durkin, and Wayne Schiess for providing the explanation of this formal phrase.

Note:
If you have information about the origins of the phrase, please share them as comments. Thanks.