According to a Pharmaceutical Journal article, myrtle originates in the Mediterranean region, where it held an important place in ancient cultures. Athenian judges wore it as an emblem of honour and authority. The wreaths worn by Greek and Roman victors, although generally described as laurel wreaths, were at first made from myrtle.
Myrtle is also alluded to in ancient religious scriptures, which associate it with the Garden of Eden. It remains important in Judaism, being one of four plants used in observing the thanksgiving festival of Succot. 
 
So, myrtle leaves are used here as a part of the religious and cultural customs and as an aromatic to fragrant the glorious journey of the patriot in the poem.