How to get browsing history using history API in Chrome extension

Pass an empty string as your query to the search() method of the chrome.history API. For example, this will log the 10 most recently visited URLs to the console:

chrome.history.search({text: '', maxResults: 10}, function(data) {
    data.forEach(function(page) {
        console.log(page.url);
    });
});

You have to put:

"permissions": [
      "history"
    ],

in you manifest.json file of the extension, and then your code can look like this:

chrome.history.search({
  'text': '',               // Return every history item....
  'startTime': oneWeekAgo,  // that was accessed less than one week ago.
  'maxResults': 100         // Optionally state a limit
},
function(historyItems) {
  // For each history item, get details on all visits.
  for (var i = 0; i < historyItems.length; ++i) {
    var url = historyItems[i].url;
     // do whatever you want with this visited url
  }
 }