There are several synonyms for the phrase "eagerly anticipate." One of the most common synonyms is "excitedly await." Other synonyms include "anxiously look forward to," "anticipate with enthusiasm," or "eagerly look ahead to." You could also use "impatiently await," "crave," or "yearn for" to express the sense of eagerness. Alternatively, you could say "await with bated breath," "long for," or "hope for eagerly." Ultimately, the choice of which synonym to use will depend on the context and the tone you want to set for the sentence or passage.