Once a page containing the link to your website is crawled, the link will generally appear in Google Search Console in 8 days.
If memory serves me correctly, I’ve seen them show up much faster and in other cases they can take longer. The last several links I tracked did indeed show up in 8 days. The most recent experiment was April 29 2016. The link displayed in Search Console May 6, 2016.
Keep in mind that getting a link and the link getting crawled are 2 separate things. Just because someone linked to you does not mean that the link was crawled; these are 2 separate things.
The 8 days may vary as well. Different websites and different niches perform differently.