Jefferson’s own account here:

It appearing in the course of these debates that the colonies of N. York, New Jersey, Pennsylvania, Delaware, Maryland, and South Carolina were not yet matured for falling from the parent stem, but that they were fast advancing to that state, it was thought most prudent to wait a while for them, and to postpone the final decision to July 1, but that this might occasion as little delay as possible a committee was appointed to prepare a declaration of independence. The committee were J. Adams, Dr. Franklin, Roger Sherman, Robert R. Livingston & myself. Committees were also appointed at the same time to prepare a plan of confederation for the colonies, and to state the terms proper to be proposed for foreign alliance.

The committee for drawing the declaration of Independence desired me to do it. It was accordingly done, and being approved by them, I reported it to the house on Friday the 28th of June when it was read and ordered to lie on the table.

[…]

Congress proceeded the same day to consider the declaration of Independence which had been reported & lain on the table the Friday preceding, and on Monday referred to a committee of the whole. The pusillanimous idea that we had friends in England worth keeping terms with, still haunted the minds of many. For this reason those passages which conveyed censures on the people of England were struck out, lest they should give them offence. The clause too, reprobating the enslaving the inhabitants of Africa, was struck out in complaisance to South Carolina and Georgia, who had never attempted to restrain the importation of slaves, and who on the contrary still wished to continue it. Our northern brethren also I believe felt a little tender under those censures; for tho’ their people have very few slaves themselves yet they had been pretty considerable carriers of them to others. The debates having taken up the greater parts of the 2d 3d & 4th days of July were, in the evening of the last, closed the declaration was reported by the committee, agreed to by the house and signed by every member present except Mr. Dickinson. As the sentiments of men are known not only by what they receive, but what they reject also, I will state the form of the declaration as originally reported.

In his memoirs, Jefferson supplies only the version presented by the Committee to Congress. Fortunately the original draft survives, in his handwriting, with annotations by Benjamin Franklin and John Adams:

To those who are celebrating it, happy 4 July!