Is it ok to put old papers on the arXiv?
Yes, this is in general OK. The main limitations on posting old papers to the arXiv are (1) copyright considerations (i.e. you must either hold the copyright, or have permission from the copyright holder to post the e-print) and (2) the approval of your co-authors, or at least the corresponding author, which can put you in a hazy gray area if you can no longer find them or they explicitly deny it. You seem to be OK on both counts.

The criteria for publishability on the arXiv are lower than a journal, and there is no previous-publication requirement or disbarment. From the arXiv primer,


  Material submitted to arXiv is expected to be of interest, relevance, and value to those disciplines. [...] Submissions are reviewed by expert moderators to verify that they are topical and refereeable scientific contributions that follow accepted standards of scholarly communication (as exemplified by conventional journal articles).


There is no requirement that work be unpublished; indeed, post-publication posting is an integral part of the self-archiving, green open access model in the post-print variety, often with a specific embargo dictated by the publisher. 

That said, each community uses the arXiv in subtly different ways, and someone who repeatedly posts old papers may get called out on it (either positively or negatively!), so if you're nervous, find someone in your field who is very active on the arXiv and ask, or simply look for precedent - it's a bit tedious but not terribly hard. For example, arXiv:1601.06054, first published in June 2014, is currently on the cond-mat front page.

One thing you should do is make sure that your metadata is pristine and complete, and to get it right the first time. This includes the DOI and journal reference - you're not there to hide anything, you're there to make your research more accessible and discoverable, and the way you do that is by having good metadata. A comment saying that this is a late posting of an old paper would not go amiss - it will defuse the people who see the posting and think it's new and would otherwise be disappointed or annoyed.

And, of course, if you're looking to make your research discoverable online, think carefully through your online presence - arXiv, Google Scholar, ResearchGate, Academia.edu, Dissemin, Mendeley, or whatever services you choose to use - and make sure that they're all what you want them to be.