<p>We have simple web-based data entry internal business app.
Now business wants to be able to attach a document to a row in the database that represents business entity. Document can be Word, Excel, PDF.</p>

<p>How can we do that?</p>

<p>I think creating yet another home grown document management system is not a good idea.
Instead we can try to use an third party document management system and integrate tightly form our app.
Ideally all user interface will stay within application, without going to an external system.
Is sharepoint or documentum capable of doing it? 
What other options are there?</p>

<p>The application platform is Java/Websphere. We ave both Windows and Unix infrastructure available.</p>

I think any document management system can do what you are requesting. At one time we did something similar with Sharepoint. The systems expose an API that allows you to query documents that are stored. Exactly how the integration happens depends on the solution you go for.
You need to consider the platform on which your current system is built when choosing because different solutions support different integration technologies. For instance, if your current system uses .NET then Sharepoint would be easy to integrate.
Many document management systems use a backend database like SQL server and integration could be as easy as querying the backend database from your application.