Hey, My Google webmaster tool has shown backlink after 20 day but it still not appear in Google when I use Google to check backlink of my site. So I think it is difficult to say the time. Thanks
Use Google webmasters tool to check your back link. else check it manually in search engine link:yoursite.com -site:yoursite.com
It depends on how regularly the spiders visit the site where the backlink has been placed. Thats why its important to be selective about where you place your links...