In this scene, the Duke is trying to convince his compatriots that traveling to the woods, far from being a form of self-imposed exile, is actually a desirable action. By speaking the lines in verse, his speech is elevated, and thereby more romantic and poetic.
Speaking in verse, as opposed to prose, lends itself to a lilting and rhythmic speech, since iambic pentameter is a very rhythmic meter that relies upon gentle emphasis of every other syllable. This serves as an elocutionary device that helps him to persuade his men that they should be pleased with his leadership and their removal from court to live in the Forest of Arden. The use of verse can be seen as a parallel of the change of setting to the forest as well: removal to a place out of the ordinary, underscored by the use of an uncommon form of speaking (i.e. in iambic pentameter).