Theoretical integration is unknown to me, and i suspect that many I/Os have not yet heard of scrum and agile. These are relatively new even in their native industry(software).
If i had to write my comprehensive exam paper on it, I'd pitch you two models. First, an oldie but a goldie, the Job Characteristics model (Hackman and Oldham). This model has identified reliable job environment features that tend to drive engagement. You could map these features onto some of the features of an agile environment:
Skill variety (agile can offer that);
Task identity (if they let you see through your project, and the execs don't override creative control, this may be available in
Task significance (this is probably independent of agile; may or may not get this)
Autonomy (agile can really offer this for the development team; this is probably the number one reason agile may be effective because it
separates the development team from the command and control of
management that is typical of waterfall methodologies)
Feedback (i think this is one of the goals of agile is more quick and dirty feedback on your prototypes; anyway feedback motivates people)
The second pitch I would make is a social psychological/sociological theory referred to as social exchange theory (e.g., Blau). The core of this theory is that people develop certain quality relationships with others they exchange with. The way this exchange occurs and how frequently can affect relationship quality. There may be two really general types of relationships: economic and social. Economic exchanges are highly equal, visible, short-term and focused on the thing being exchanged (this characterizes a lot of employee-employer relationships). Social exchanges are less concerned with the urgency and equality of transactions, and are more concerned with longevity, empathy and belonging in the relationship (many organizations try to create this with culture; people want this because it can cause employees to give effort selflessly).
Agile may in some cases appeal to this social exchange type of relationship. A lot of effort, creativity, and risk is exchanged and tolerated among teammates without any immediate monetary reward or sometimes without much awareness from management. Due to the frequency of exchanges with team members in agile methodology, perhaps the relationship development process is accelerated. This would yield more committed and engaged team members, at least when they're working within those teams.
Oh, and the goal setting theorists will insist that it boils down to frequently setting challenging, specific and committed to goals.
Hope this helps.