Yes, in the vast majority of cases this is not a problem at all. To quote the EPrints Self-Archiving FAQ:
Texts that an author has himself written are his own intellectual property. The author holds the copyright and is free to give away or sell copies, on-paper or on-line (e.g., by self-archiving), as he sees fit. For example, the pre-refereeing preprint can always be legally self-archived.
Self-archiving of one's own, non-plagiarized texts is in general legal in all cases but two. The first of these two exceptions is irrelevant to the kind of self-archiving BOAI is concerned with, and for the second there is a legal alternative.
Exception 1: Where exclusive copyright in a "work for hire" has been transfered by the author to a publisher -- i.e., the author has been paid (or will be paid royalties) in exchange for the text -- the author may not self-archive it. (...)
Exception 1 is irrelevant [for this case, which is concerned] only with peer-reviewed research, for which the author is paid nothing, and no royalty revenue or author fee is expected, sought, or paid.
Exception 2: Where exclusive copyright has been assigned by the author to a journal publisher for a peer-reviewed draft, copy-edited and accepted for publication by that journal, then that draft may not be self-archived by the author (without the publisher's permission). (...)
Of the nearly 10,000 journals surveyed over 90% are already "green" (i.e., they have already given their official green light to author self-archiving: 62% for postprints, 29% for preprints). Many of the remaining 9% "gray" journals will agree if the author asks.