When Aristotle discusses Eudaimonia, we will find it beneficial to consider that his notions compare closely to what Jefferson is suggesting by Happiness in The Declaration of Independence. Eudaimonia doesn't translate directly to Happiness, but a consideration of the Lockean discussions that give the Declaration its context, suggest that in this matter Jefferson does indeed sympathize closely with Aristotle.
In the following passage, Anthony Kenny characterizes the concept of Eudaimonia in Aristotle's Nichomachean Ethics and the Eudemian Ethics:
In Book X [of the Nicomachean Ethics] Aristotle finally answers his long-postponed question about the nature of happiness. Happiness, we were told early on in the treatise, is the activity of soul in accordance with virtue, and if there are several virtues, in accordance with the best and most perfect virtue. Now we know that there are both moral and intellectual virtues, and that the latter are superior; and among the intellectual virtues, understanding is superior to wisdom. Supreme happiness, then, is activity in accordance with understanding; it is to be found in science and philosophy. Happiness is not exactly the same as the pursuit of science and philosophy, but it is closely related to it: we are told that understanding is related to philosophy as knowing is to seeking. Happiness, then, in a way which remains to some extent obscure, is to be identified with the enjoyment of the fruits of philosophical inquiry.To many people this seems an odd, indeed perverse, thesis. It is not quite as odd as it sounds, because the Greek word for happiness,’eudaimonia', does not mean quite the same as its English equivalent, just as 'arete’ did not mean quite the same as virtue. Perhaps 'a worthwhile life' is the closest we can get to its meaning in English. Even so, it is hard to accept Aristotle’s thesis that the philosopher's life is the only really worthwhile one, and this is so whether one finds the claim endearing or finds it arrogant. Aristotle himself seems to have had second thoughts about it. Elsewhere in the Nicomachean Ethics he says that there is another kind of happiness which consists in the exercise of wisdom and the moral virtues. In the Eudemian Ethics his ideal life consists of the exercise of all the virtues, intellectual and moral; but even there, philosophical contemplation occupies a dominant position in the life of the happy person, and sets the standard for the exercise of the moral virtues.
Whatever choice or possession of natural goods - health and strength, wealth, friends and the like - will most conduce to the contemplation of God is best: this is the finest criterion. But any standard of living which either through excess or defect hinders the service and contemplation of God is bad.
Both of Aristotle's Ethics end on this exalted note. The contemplation commended by the Nicomachean Ethics is described as a superhuman activity of a divine part of us. Aristotle's final word here is that in spite of being mortal, we must make ourselves immortal so far as we can.--Anthony Kenny, An Illustrated Brief History of Western Philosophy, Blackwell, 2006
Please click HERE for more on how Locke fits into this discussion.