Dante's Divine Comedy is considered to be a comedy and not a tragedy for several reasons. The most important one is that it ends happily - the protagonist goes through Hell (Inferno), Purgatory (Purgatorio), and finally comes into Heaven (Paradiso) in the end. Tragedies are characterized by tragic and sad endings - usually with some characters dying. This is not the case in Divine Comedy - the protagonist manages to enter Heaven and finally understand the meaning of life.
Additionally, Dante named his work Comedy in order to show everyone that comedies don't have to be written using low style only (tragedies were always considered something elitist, using high style difficult to understand). He wrote Divine Comedy using elevated, sophisticated language in order to show it can be done.