How to cite a work in a manuscript that is under review? I have two manuscripts that I am ready to submit in two different journals. 

In the first manuscript, I have developed two models to be used for my research. Both of them are new and are an upgrade to the currently used models.

In the second manuscript, I have used one of the models developed in the first manuscript and have carried out an elaborate study. However, I am unsure on how to cite the first manuscript in the second. 

Can I cite a submitted manuscript as "under review" in another manuscript? What's the correct procedure for citing under review works?
Yes.  Under review or "in review" are normal and I have used them myself when publishing several papers near simultaneously.  (They were separate enough, different chemistries, that I thought made sense to cut into separate articles.  But, for someone interested in the general area, they likely would want the citation.)  It is to be understood that "under review" does not mean it will EVER get published (but likely will).  You are doing the best you can, at the time.  If the paper never makes it out or shifts to another journal, so be it.

You may also see citations that say "in press" (meaning accepted, but you are lacking the issue and page numbers).  I have even used "in preparation for" and listed the journal I planned to, and did submit to.  And I've even used "unpublished" for work that never saw the light of day (e.g. another worker's parallel chemistry study that was pretty finished, yet shelved as uninteresting...but was relevant to a chemistry to chemistry discussion.)*

The key thing is that you are not trying to get away with anything nefarious.  You are simply doing your best to give citations to other work.  And that will include some not-yet archived research.  You just do the best you can, at the time you submit.

[Obviously if you are claiming some super insight and your current paper is fundamentally dependent on the other work, the editor/reviewer may cavitate and reject.  But if you are just doing good stuff and other work is comparative, not dependent, people will appreciate the citation, not resent it.]

*Even this still has a use.  For one, a simple (non-controversial) insight may be shared, that is scientifically relevant.  In addition, if anyone ever really cares, they might still track down the author.  I. R. Lazyguy; structure of unimportant chemical; 1989; Random Federal Agency; unpublished.