Benefits

Typical benefits that you will see when you move to or improve an Agile process are:

Improved Quality & Lower Defects

Whole team (BA, dev and QA) working together during the iteration reduces defects.
Acceptance tests created early by BA/QA reduces defects.
Unit testing reduces defects.

Good visibility and control through open process framework provides management with better information to make better choices about what to invest in and delivery timelines.
Direct product management involvement leads to better choices about what to work on.
Iteration review allows for early identification of usability, missing requirements and better understanding of system evolution.
Iterative delivery allows system to evolve as it is built.

Iterative delivery and just-in-time requirements allow reduces time between idea generation and delivery of working software.
Rolling-wave adaptive planning allows for course corrections and injection of high-value features.
Lean manufacturing principles (that apply to software) have a long track record of success.

Team rooms provide very large boost in productivity and focus. Some reports document 2x.
Engineering best practices (unit test, automated testing, design alternatives, continuous integration, delayed commitment) reduces wasted work.
Dedicated team enables better focus on iteration goals (no changes in focus or priority).
Iteration retrospective provides regular opportunity to improve productivity.
Self-organizing team allows improved work distribution.

Improved productivity as above.
Less work is wasted fixing avoidable defects
Reduced maintenance costs: Systems built with evolutionary design tend to be simpler with less code. Pair programming accelerates this benefit.