Charles F. Benjamin wrote the account of Meade’s accension to command of the Army of the Potomac that appeared in Battles and Leaders of the Civil War. (You can find it in volume III, pages 239-243).

Several Rosengartens are buried in Laurel Hill Cemetery, not far from Meade’s grave. The grave of Major Adolph Rosengarten, who died at the Battle of Stones River, is in the foreground. The grave of his brother, Joseph, is in the background, also marked by a flag.
While doing research with the microfilmed version of Meade’s papers at the Army Heritage Center in Carlisle, I recently came across a typescript copy of a letter that this same Charles Benjamin had written on August 7, 1883 to Major Joseph G. Rosengarten of Philadelphia. Rosengarten had fought with the 121st Pennsylvania and later served on Major General John F. Reynolds’ staff. (Like George Meade, he was buried in Laurel Hill Cemetery. It’s a small world.) No doubt the Reynolds connection explains Rosengarten’s interest in the subject matter of Benjamin’s letter.
Benjamin had been serving under Major General Seth Williams in the days leading up to Gettysburg. (Like me, Williams was a native of Augusta, Maine. He was well liked and efficient and served as Meade’s assistant adjutant general.) This is what Benjamin wrote to Rosengarten:
At the time mentioned I was serving as a clerk at the general Head Quarters and was employed in close attendance upon Seth Williams, the Adjutant General of the Army of the Potomac.
Shortly after taking notice of Genl. Meade in front of his tent, with a group of visiting officers, together with Butterfield, Ingalls, Hunt, Williams and others of our staff about him, I went back in our own little office tent to continue some writing I was doing for General Williams. While so engaged the open tent flap was pushed further back, and Genl. Meade came in, ushering Genl. Reynolds. The first thing that struck me was the contrast between Meade, in soldiers trousers and blouse with the rim of a slouched hat turned down to screen his eyes, (or spectacles) from the sun, and the neat figure of Reynolds, who had a close fitting frock coat (I think it was—if a blouse it was dressy looking and tight fitting) and a kepi which he held in his hand during the conversation. When I saw who the visitors were I wanted to leave the tent, but being screened by the travelling desk which stood on the table between me and the door, I had not been perceived and Meade began so soon and talked so fast, that I concluded the best thing to do was to keep on writing and pay no attention to what was said. But Meade being a man of impetuous speech always and doubtless having in mind that Williams was at the Commanding General’s tent, made me a listener in spite of myself. He began immediately on getting inside, in language substantially as follows: “Reynolds, I have been very anxious to have a talk with you since I have been put in command – I assure you I never dreamed that the command was to be given to me. I had supposed, as everybody in the army did, that it would fall to you when a change was made. I never would have accepted it if there had been a choice left me, but it as put upon me as an imperative order and I had to take it. I wanted you to understand this, that I am not here by my will, and I count on you, above all others, for the support that I would have given you, if you had been placed in the situation that I am in.”
The reply of Reynolds, naturally, did not so much interest me, as what I had heard said by Meade, but I am (sure) that the following gives the spirit and substance if not the very words –“General in my opinion the command has fallen where it ought to fall. If it had come to me in the same way, I should have been obliged to take it, but I am glad that it did not. I understand the difficulties of your position and you may rely upon me to serve you faithfully.” They then entered upon a conversation, in which Meade explained the position of the troops en route; the nature of the communications he had received from Washington, and such information as had come in about the enemy. These were matters that did not at the moment interest me, as I knew them already and hence I have retained scarcely any recollection of the language used. But when Meade summed up the words I have quoted in “The Nation”, I was interested of course, as indicating where the battle was likely to be fought. I had heard so much of Pipe Creek as the probable site of the coming engagement during the last days of Hooker and the first days of Meade, that the mention of Gettysburg as a probably battle-field was a revelation to me and hence this part of the conversation was impressed upon me. Furthermore, when Meade’s failure to arrest Lee’s retreat led to charges which (in their ultimate form) alleged that Meade had never thought about Gettysburg at all, and that his surprise and ignorance of the ground were sufficient to explain his desire to retreat to Pipe Creek, I thought it proper to mention to Seth Williams what I had heard Meade say to Reynolds, as quoted in “The Nation.” Shortly afterwards, Williams went out and when he came back, he asked me to write out a careful memorandum of Meade’s exact words, as nearly as I could recall them – I did so, and am morally certain that the memorandum was for Meade himself, as anybody would be who knew the characteristics of Seth Williams.

Colonel James Hardie, the man Secretary of War Edwin Stanton sent to tell Meade he had been placed in command of the Army of the Potomac.
P.S. In my printed biographical sketch of the late Col. Hardie, who bore the order to Genl. Meade to take over command from Genl. Hooker, I mention Meade’s surprise at seeing Hardie in his tent with a message from Washington, his incredulity at the nature of the order and his excited demand to know why he was chosen instead of Reynolds. Hardie told the story in full; the anxiety of Secy. Stanton lest Hooker might evade compliance with the order till after the battle, if opportunities were given him; the extraordinary course of sending Hardie to privately to Meade and making Meade go immediately and take command before Hooker could now what was afloat and all the rest of the details of the unusual episode.
(You can find that biographical sketch here.)
The next week Benjamin wrote a follow-up to Rosengarten to fine-tune his recollections. The text is here. I have yet to find Benjamin’s letter in The Nation, but I assume it concerns his memory of Meade mentioning Gettysburg as a potential point of battle in his conversation with Reynolds.