Like ads, boosted Page posts will be reviewed by Facebook. Boosted Page posts are generally reviewed in less than 60 minutes. However, in some instances, it may take longer. Just like with posts you don't boost, your posts should show up in the News Feeds of some of the people who like your Page right away.
If you're worried your post won't be approved on time, you can always schedule your post early. Once scheduled, click Boost Post. Your boost should start on the day your post is scheduled to begin.