All thats required is this kind of stanza in your build.xml:
<property environment="env"/>
<target name="-post-build" >
<copy todir="bin">
<fileset dir="bin">
<include name="myappname-*.apk"/>
</fileset>
<globmapper from="myappname-*.apk" to="myappname-*.${env.BUILD_NUMBER}.apk"/>
</copy>
</target>
As you can see I'm also naming the final apk file with the Jenkins build number environment variable. There are a lot more other env vars that Jenkins sets that you can use.
Also note the reason I've used the globmapper is that this will work for both the debug and release build targets that are pre-defined in the standard android project ant build configs. This means you can have Hudson build configs for both debug and release.
If you want your release apk to be properly signed, you need to create a certificate and then point your ant build at it (ant.properties):
key.store=path/to/my.keystore
key.alias=mykeystore
If you don't want to type in the password for each build, you can add the following to your local.properties:
key.store.password=secretpasswd
key.alias.password=secretpasswd
And also add the passwd properties to your Jenkins config (click "Advanced" button in the "Invoke Ant" section of your build config). This way you never have to check your keystore passwords into version control.
Oh as a bonus, if you want to be able to access the build information within your apps code at runtime, you can stash this in a string value by putting something
like this in your build.xml:
<property environment="env"/>
<target name="-pre-build">
<echo file="res/values/buildtag.xml"><![CDATA[<?xml version="1.0" encoding="utf-8"?>
<resources>
<string name="build_version">ABCXYZ123</string>
</resources>
]]>
</echo>
<replace file="res/values/buildtag.xml" token="ABCXYZ123" value="${env.BUILD_TAG}"/>
</target><echo file="res/values/buildtag.xml"><![CDATA[<?xml version="1.0" encoding="utf-8"?>
<resources>
<string name="build_version">ABCXYZ123</string>
</resources>
]]>
</echo>
<replace file="res/values/buildtag.xml" token="ABCXYZ123" value="${env.BUILD_TAG}"/>
